comparison of spmds and biotic samplers … biotic samplers using gnostic analysis ... geometry...

39
COMPARISON OF SPMDs COMPARISON OF SPMDs AND BIOTIC SAMPLERS AND BIOTIC SAMPLERS USING GNOSTIC ANAL USING GNOSTI YSIS C ANALYSIS Institute of Public Health, Ostrava, Czech Republi Institute of Public Health, Ostrava, Czech Republic National reference laboratory for POPs National reference laboratory for POPs Tomas Ocelka, Tomas Ocelka, Pavel Pavel Kovanic Kovanic Tomas. Tomas [email protected] [email protected] 1 1

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Page 1: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

COMPARISON OF SPMDsCOMPARISON OF SPMDsAND BIOTIC SAMPLERSAND BIOTIC SAMPLERS

USING GNOSTIC ANALUSING GNOSTI YSISC ANALYSIS

Institute of Public Health Ostrava Czech RepubliInstitute of Public Health Ostrava Czech RepublicNational reference laboratory for POPsNational reference laboratory for POPs

Tomas OcelkaTomas Ocelka PavelPavel KovanicKovanic

TomasTomas OcelkazuovaczOcelkazuovacz

11

1

22

TOPICSTOPICS

Sampling methods to beSampling methods to be comparedcompared

Objects of measuringObjects of measuring Problems of analysisProblems of analysis Gnostic analysisGnostic analysis Methodsrsquo features to be comparedMethodsrsquo features to be compared Results of comparisonResults of comparison

2

33

Geographic locationGeographic location

3

ndash

ndash

ndash -

ndash

ndash

ndashndash

Centre laboratoriesCentre laboratories accreditationaccreditation

Personnel over 140 5+Person 2 workplacesnel over 140 5+2 workplaces According to ČSN EN ISOIEC 17According 025to ČSN EN ISOIEC 17 025

ndash Over 200 paraOver 200 p metersarameters PCDDFs PCBs OCPs PBDE hellipPCDDFs PCBs OCPs PBDE hellip

ndash Recognized by ILAC EA IAFRecognized by ILAC EA IAF Sampling and TestingSampling and Testing

ndash IntegralIntegral - waterwater SPMDsSPMDs DGTsDGTs POCIPOC SIS

ndash Biotic organiBioti smsc organisms IntercalibrationIntercalibration

ndash Czech + InternationalCzech + International Data analysis (univariatemultivariate)Data analysis (univariatemultivariate)

ndash StatisStati ticalsticalndash GnosticGnostic

44

4

InstrumentatiInstrumenta ontion (worth over 6 mil USD)(worth over 6 mil USD)

GC-MSMS (ion-trap)

-GCQ Polaris

-Since 1996 (starting to POPs issue)

GC-HRMS (POPs)

- MAT 95XP

- since 2003

LC-MSMS (pharmacy pesticides)

- ThermoFinigan

- since 2006 55

5

ndash

ndash

ndashndash ndash

Data source for comparison ofData source for comparison of methodsmethods

All rivers within Czech RepuAll rivers wi blicthin Czech Republic scale (15)scale (15)

21 sampling pr21 sampling p ofilesrofiles Complementary to bioticComplementary to biotic

sampling system (since 1999)sampling system (since 1999) with abiotic (SPMDs DGTswith abiotic (SPMDs DGTs POCIS)POCIS) ndashndash sincsi e 2003nce 2003

AimsAimsndash Pilot application 2 years beforePilot application 2 years before

routine applicationroutine application ndash Parallel exposure of DreissenaParallel exposure of Dreissena

Polymorpha Benthos PlantsPolymorpha Benthos Plantsndash POPs (basic OCPs PCBs)POPs (basic OCPs PCBs)ndash POPs (other PCBsPOPs (other PCBs ndash coc ngong

PCDDFs PAHs PBDEPCDDFs PAHs PBD s)Es)

66

6

SAMPLING METHODSSAMPLING METHODSTO BE COMPAREDTO BE COMPARED

ThreeThree bioticbiotic methodsmethods BentosBentos DreissenaDreissena PlantsPlantsOneOne abioticabiotic methmet od SPMDhod SPMD(Semipermeable Membrane Measuring(Semipermeable Membrane Measuring

Device)Device)77

7

The selectionThe selection

Concentrations of selected permanentConcentrations of selected permanentorganic pollutants (POPs) in severalorganic pollutants (POPs) in severallocations of Elbe river in Czech Republiclocations of Elbe river in Czech Republic

ppDDEppDDE PCB138 PCB180 PCB138 PCB180 PCB101 PCB2831PCB101 PCB2831 ppDDTppDDT ppDDDppDDD PCB52 PCB118 PCB52 PCB118

88

8

PROBLEMS OF ANALYSISPROBLEMS OF ANALYSIS

Small data samplesSmall data samples Different mean concentrationsDifferent mean concentrations Strong vaStrong v riabilityariability Different length of data vectorsDifferent length of data vectors Data censoring (Data censoring (egeg data below the LOD)data below the LOD) NonNon--homogeneous and outlying datahomogeneous and outlying data

99

9

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 2: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

22

TOPICSTOPICS

Sampling methods to beSampling methods to be comparedcompared

Objects of measuringObjects of measuring Problems of analysisProblems of analysis Gnostic analysisGnostic analysis Methodsrsquo features to be comparedMethodsrsquo features to be compared Results of comparisonResults of comparison

2

33

Geographic locationGeographic location

3

ndash

ndash

ndash -

ndash

ndash

ndashndash

Centre laboratoriesCentre laboratories accreditationaccreditation

Personnel over 140 5+Person 2 workplacesnel over 140 5+2 workplaces According to ČSN EN ISOIEC 17According 025to ČSN EN ISOIEC 17 025

ndash Over 200 paraOver 200 p metersarameters PCDDFs PCBs OCPs PBDE hellipPCDDFs PCBs OCPs PBDE hellip

ndash Recognized by ILAC EA IAFRecognized by ILAC EA IAF Sampling and TestingSampling and Testing

ndash IntegralIntegral - waterwater SPMDsSPMDs DGTsDGTs POCIPOC SIS

ndash Biotic organiBioti smsc organisms IntercalibrationIntercalibration

ndash Czech + InternationalCzech + International Data analysis (univariatemultivariate)Data analysis (univariatemultivariate)

ndash StatisStati ticalsticalndash GnosticGnostic

44

4

InstrumentatiInstrumenta ontion (worth over 6 mil USD)(worth over 6 mil USD)

GC-MSMS (ion-trap)

-GCQ Polaris

-Since 1996 (starting to POPs issue)

GC-HRMS (POPs)

- MAT 95XP

- since 2003

LC-MSMS (pharmacy pesticides)

- ThermoFinigan

- since 2006 55

5

ndash

ndash

ndashndash ndash

Data source for comparison ofData source for comparison of methodsmethods

All rivers within Czech RepuAll rivers wi blicthin Czech Republic scale (15)scale (15)

21 sampling pr21 sampling p ofilesrofiles Complementary to bioticComplementary to biotic

sampling system (since 1999)sampling system (since 1999) with abiotic (SPMDs DGTswith abiotic (SPMDs DGTs POCIS)POCIS) ndashndash sincsi e 2003nce 2003

AimsAimsndash Pilot application 2 years beforePilot application 2 years before

routine applicationroutine application ndash Parallel exposure of DreissenaParallel exposure of Dreissena

Polymorpha Benthos PlantsPolymorpha Benthos Plantsndash POPs (basic OCPs PCBs)POPs (basic OCPs PCBs)ndash POPs (other PCBsPOPs (other PCBs ndash coc ngong

PCDDFs PAHs PBDEPCDDFs PAHs PBD s)Es)

66

6

SAMPLING METHODSSAMPLING METHODSTO BE COMPAREDTO BE COMPARED

ThreeThree bioticbiotic methodsmethods BentosBentos DreissenaDreissena PlantsPlantsOneOne abioticabiotic methmet od SPMDhod SPMD(Semipermeable Membrane Measuring(Semipermeable Membrane Measuring

Device)Device)77

7

The selectionThe selection

Concentrations of selected permanentConcentrations of selected permanentorganic pollutants (POPs) in severalorganic pollutants (POPs) in severallocations of Elbe river in Czech Republiclocations of Elbe river in Czech Republic

ppDDEppDDE PCB138 PCB180 PCB138 PCB180 PCB101 PCB2831PCB101 PCB2831 ppDDTppDDT ppDDDppDDD PCB52 PCB118 PCB52 PCB118

88

8

PROBLEMS OF ANALYSISPROBLEMS OF ANALYSIS

Small data samplesSmall data samples Different mean concentrationsDifferent mean concentrations Strong vaStrong v riabilityariability Different length of data vectorsDifferent length of data vectors Data censoring (Data censoring (egeg data below the LOD)data below the LOD) NonNon--homogeneous and outlying datahomogeneous and outlying data

99

9

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 3: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

33

Geographic locationGeographic location

3

ndash

ndash

ndash -

ndash

ndash

ndashndash

Centre laboratoriesCentre laboratories accreditationaccreditation

Personnel over 140 5+Person 2 workplacesnel over 140 5+2 workplaces According to ČSN EN ISOIEC 17According 025to ČSN EN ISOIEC 17 025

ndash Over 200 paraOver 200 p metersarameters PCDDFs PCBs OCPs PBDE hellipPCDDFs PCBs OCPs PBDE hellip

ndash Recognized by ILAC EA IAFRecognized by ILAC EA IAF Sampling and TestingSampling and Testing

ndash IntegralIntegral - waterwater SPMDsSPMDs DGTsDGTs POCIPOC SIS

ndash Biotic organiBioti smsc organisms IntercalibrationIntercalibration

ndash Czech + InternationalCzech + International Data analysis (univariatemultivariate)Data analysis (univariatemultivariate)

ndash StatisStati ticalsticalndash GnosticGnostic

44

4

InstrumentatiInstrumenta ontion (worth over 6 mil USD)(worth over 6 mil USD)

GC-MSMS (ion-trap)

-GCQ Polaris

-Since 1996 (starting to POPs issue)

GC-HRMS (POPs)

- MAT 95XP

- since 2003

LC-MSMS (pharmacy pesticides)

- ThermoFinigan

- since 2006 55

5

ndash

ndash

ndashndash ndash

Data source for comparison ofData source for comparison of methodsmethods

All rivers within Czech RepuAll rivers wi blicthin Czech Republic scale (15)scale (15)

21 sampling pr21 sampling p ofilesrofiles Complementary to bioticComplementary to biotic

sampling system (since 1999)sampling system (since 1999) with abiotic (SPMDs DGTswith abiotic (SPMDs DGTs POCIS)POCIS) ndashndash sincsi e 2003nce 2003

AimsAimsndash Pilot application 2 years beforePilot application 2 years before

routine applicationroutine application ndash Parallel exposure of DreissenaParallel exposure of Dreissena

Polymorpha Benthos PlantsPolymorpha Benthos Plantsndash POPs (basic OCPs PCBs)POPs (basic OCPs PCBs)ndash POPs (other PCBsPOPs (other PCBs ndash coc ngong

PCDDFs PAHs PBDEPCDDFs PAHs PBD s)Es)

66

6

SAMPLING METHODSSAMPLING METHODSTO BE COMPAREDTO BE COMPARED

ThreeThree bioticbiotic methodsmethods BentosBentos DreissenaDreissena PlantsPlantsOneOne abioticabiotic methmet od SPMDhod SPMD(Semipermeable Membrane Measuring(Semipermeable Membrane Measuring

Device)Device)77

7

The selectionThe selection

Concentrations of selected permanentConcentrations of selected permanentorganic pollutants (POPs) in severalorganic pollutants (POPs) in severallocations of Elbe river in Czech Republiclocations of Elbe river in Czech Republic

ppDDEppDDE PCB138 PCB180 PCB138 PCB180 PCB101 PCB2831PCB101 PCB2831 ppDDTppDDT ppDDDppDDD PCB52 PCB118 PCB52 PCB118

88

8

PROBLEMS OF ANALYSISPROBLEMS OF ANALYSIS

Small data samplesSmall data samples Different mean concentrationsDifferent mean concentrations Strong vaStrong v riabilityariability Different length of data vectorsDifferent length of data vectors Data censoring (Data censoring (egeg data below the LOD)data below the LOD) NonNon--homogeneous and outlying datahomogeneous and outlying data

99

9

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 4: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

ndash

ndash

ndash -

ndash

ndash

ndashndash

Centre laboratoriesCentre laboratories accreditationaccreditation

Personnel over 140 5+Person 2 workplacesnel over 140 5+2 workplaces According to ČSN EN ISOIEC 17According 025to ČSN EN ISOIEC 17 025

ndash Over 200 paraOver 200 p metersarameters PCDDFs PCBs OCPs PBDE hellipPCDDFs PCBs OCPs PBDE hellip

ndash Recognized by ILAC EA IAFRecognized by ILAC EA IAF Sampling and TestingSampling and Testing

ndash IntegralIntegral - waterwater SPMDsSPMDs DGTsDGTs POCIPOC SIS

ndash Biotic organiBioti smsc organisms IntercalibrationIntercalibration

ndash Czech + InternationalCzech + International Data analysis (univariatemultivariate)Data analysis (univariatemultivariate)

ndash StatisStati ticalsticalndash GnosticGnostic

44

4

InstrumentatiInstrumenta ontion (worth over 6 mil USD)(worth over 6 mil USD)

GC-MSMS (ion-trap)

-GCQ Polaris

-Since 1996 (starting to POPs issue)

GC-HRMS (POPs)

- MAT 95XP

- since 2003

LC-MSMS (pharmacy pesticides)

- ThermoFinigan

- since 2006 55

5

ndash

ndash

ndashndash ndash

Data source for comparison ofData source for comparison of methodsmethods

All rivers within Czech RepuAll rivers wi blicthin Czech Republic scale (15)scale (15)

21 sampling pr21 sampling p ofilesrofiles Complementary to bioticComplementary to biotic

sampling system (since 1999)sampling system (since 1999) with abiotic (SPMDs DGTswith abiotic (SPMDs DGTs POCIS)POCIS) ndashndash sincsi e 2003nce 2003

AimsAimsndash Pilot application 2 years beforePilot application 2 years before

routine applicationroutine application ndash Parallel exposure of DreissenaParallel exposure of Dreissena

Polymorpha Benthos PlantsPolymorpha Benthos Plantsndash POPs (basic OCPs PCBs)POPs (basic OCPs PCBs)ndash POPs (other PCBsPOPs (other PCBs ndash coc ngong

PCDDFs PAHs PBDEPCDDFs PAHs PBD s)Es)

66

6

SAMPLING METHODSSAMPLING METHODSTO BE COMPAREDTO BE COMPARED

ThreeThree bioticbiotic methodsmethods BentosBentos DreissenaDreissena PlantsPlantsOneOne abioticabiotic methmet od SPMDhod SPMD(Semipermeable Membrane Measuring(Semipermeable Membrane Measuring

Device)Device)77

7

The selectionThe selection

Concentrations of selected permanentConcentrations of selected permanentorganic pollutants (POPs) in severalorganic pollutants (POPs) in severallocations of Elbe river in Czech Republiclocations of Elbe river in Czech Republic

ppDDEppDDE PCB138 PCB180 PCB138 PCB180 PCB101 PCB2831PCB101 PCB2831 ppDDTppDDT ppDDDppDDD PCB52 PCB118 PCB52 PCB118

88

8

PROBLEMS OF ANALYSISPROBLEMS OF ANALYSIS

Small data samplesSmall data samples Different mean concentrationsDifferent mean concentrations Strong vaStrong v riabilityariability Different length of data vectorsDifferent length of data vectors Data censoring (Data censoring (egeg data below the LOD)data below the LOD) NonNon--homogeneous and outlying datahomogeneous and outlying data

99

9

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 5: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

InstrumentatiInstrumenta ontion (worth over 6 mil USD)(worth over 6 mil USD)

GC-MSMS (ion-trap)

-GCQ Polaris

-Since 1996 (starting to POPs issue)

GC-HRMS (POPs)

- MAT 95XP

- since 2003

LC-MSMS (pharmacy pesticides)

- ThermoFinigan

- since 2006 55

5

ndash

ndash

ndashndash ndash

Data source for comparison ofData source for comparison of methodsmethods

All rivers within Czech RepuAll rivers wi blicthin Czech Republic scale (15)scale (15)

21 sampling pr21 sampling p ofilesrofiles Complementary to bioticComplementary to biotic

sampling system (since 1999)sampling system (since 1999) with abiotic (SPMDs DGTswith abiotic (SPMDs DGTs POCIS)POCIS) ndashndash sincsi e 2003nce 2003

AimsAimsndash Pilot application 2 years beforePilot application 2 years before

routine applicationroutine application ndash Parallel exposure of DreissenaParallel exposure of Dreissena

Polymorpha Benthos PlantsPolymorpha Benthos Plantsndash POPs (basic OCPs PCBs)POPs (basic OCPs PCBs)ndash POPs (other PCBsPOPs (other PCBs ndash coc ngong

PCDDFs PAHs PBDEPCDDFs PAHs PBD s)Es)

66

6

SAMPLING METHODSSAMPLING METHODSTO BE COMPAREDTO BE COMPARED

ThreeThree bioticbiotic methodsmethods BentosBentos DreissenaDreissena PlantsPlantsOneOne abioticabiotic methmet od SPMDhod SPMD(Semipermeable Membrane Measuring(Semipermeable Membrane Measuring

Device)Device)77

7

The selectionThe selection

Concentrations of selected permanentConcentrations of selected permanentorganic pollutants (POPs) in severalorganic pollutants (POPs) in severallocations of Elbe river in Czech Republiclocations of Elbe river in Czech Republic

ppDDEppDDE PCB138 PCB180 PCB138 PCB180 PCB101 PCB2831PCB101 PCB2831 ppDDTppDDT ppDDDppDDD PCB52 PCB118 PCB52 PCB118

88

8

PROBLEMS OF ANALYSISPROBLEMS OF ANALYSIS

Small data samplesSmall data samples Different mean concentrationsDifferent mean concentrations Strong vaStrong v riabilityariability Different length of data vectorsDifferent length of data vectors Data censoring (Data censoring (egeg data below the LOD)data below the LOD) NonNon--homogeneous and outlying datahomogeneous and outlying data

99

9

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 6: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

ndash

ndash

ndashndash ndash

Data source for comparison ofData source for comparison of methodsmethods

All rivers within Czech RepuAll rivers wi blicthin Czech Republic scale (15)scale (15)

21 sampling pr21 sampling p ofilesrofiles Complementary to bioticComplementary to biotic

sampling system (since 1999)sampling system (since 1999) with abiotic (SPMDs DGTswith abiotic (SPMDs DGTs POCIS)POCIS) ndashndash sincsi e 2003nce 2003

AimsAimsndash Pilot application 2 years beforePilot application 2 years before

routine applicationroutine application ndash Parallel exposure of DreissenaParallel exposure of Dreissena

Polymorpha Benthos PlantsPolymorpha Benthos Plantsndash POPs (basic OCPs PCBs)POPs (basic OCPs PCBs)ndash POPs (other PCBsPOPs (other PCBs ndash coc ngong

PCDDFs PAHs PBDEPCDDFs PAHs PBD s)Es)

66

6

SAMPLING METHODSSAMPLING METHODSTO BE COMPAREDTO BE COMPARED

ThreeThree bioticbiotic methodsmethods BentosBentos DreissenaDreissena PlantsPlantsOneOne abioticabiotic methmet od SPMDhod SPMD(Semipermeable Membrane Measuring(Semipermeable Membrane Measuring

Device)Device)77

7

The selectionThe selection

Concentrations of selected permanentConcentrations of selected permanentorganic pollutants (POPs) in severalorganic pollutants (POPs) in severallocations of Elbe river in Czech Republiclocations of Elbe river in Czech Republic

ppDDEppDDE PCB138 PCB180 PCB138 PCB180 PCB101 PCB2831PCB101 PCB2831 ppDDTppDDT ppDDDppDDD PCB52 PCB118 PCB52 PCB118

88

8

PROBLEMS OF ANALYSISPROBLEMS OF ANALYSIS

Small data samplesSmall data samples Different mean concentrationsDifferent mean concentrations Strong vaStrong v riabilityariability Different length of data vectorsDifferent length of data vectors Data censoring (Data censoring (egeg data below the LOD)data below the LOD) NonNon--homogeneous and outlying datahomogeneous and outlying data

99

9

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 7: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

SAMPLING METHODSSAMPLING METHODSTO BE COMPAREDTO BE COMPARED

ThreeThree bioticbiotic methodsmethods BentosBentos DreissenaDreissena PlantsPlantsOneOne abioticabiotic methmet od SPMDhod SPMD(Semipermeable Membrane Measuring(Semipermeable Membrane Measuring

Device)Device)77

7

The selectionThe selection

Concentrations of selected permanentConcentrations of selected permanentorganic pollutants (POPs) in severalorganic pollutants (POPs) in severallocations of Elbe river in Czech Republiclocations of Elbe river in Czech Republic

ppDDEppDDE PCB138 PCB180 PCB138 PCB180 PCB101 PCB2831PCB101 PCB2831 ppDDTppDDT ppDDDppDDD PCB52 PCB118 PCB52 PCB118

88

8

PROBLEMS OF ANALYSISPROBLEMS OF ANALYSIS

Small data samplesSmall data samples Different mean concentrationsDifferent mean concentrations Strong vaStrong v riabilityariability Different length of data vectorsDifferent length of data vectors Data censoring (Data censoring (egeg data below the LOD)data below the LOD) NonNon--homogeneous and outlying datahomogeneous and outlying data

99

9

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 8: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

The selectionThe selection

Concentrations of selected permanentConcentrations of selected permanentorganic pollutants (POPs) in severalorganic pollutants (POPs) in severallocations of Elbe river in Czech Republiclocations of Elbe river in Czech Republic

ppDDEppDDE PCB138 PCB180 PCB138 PCB180 PCB101 PCB2831PCB101 PCB2831 ppDDTppDDT ppDDDppDDD PCB52 PCB118 PCB52 PCB118

88

8

PROBLEMS OF ANALYSISPROBLEMS OF ANALYSIS

Small data samplesSmall data samples Different mean concentrationsDifferent mean concentrations Strong vaStrong v riabilityariability Different length of data vectorsDifferent length of data vectors Data censoring (Data censoring (egeg data below the LOD)data below the LOD) NonNon--homogeneous and outlying datahomogeneous and outlying data

99

9

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 9: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

PROBLEMS OF ANALYSISPROBLEMS OF ANALYSIS

Small data samplesSmall data samples Different mean concentrationsDifferent mean concentrations Strong vaStrong v riabilityariability Different length of data vectorsDifferent length of data vectors Data censoring (Data censoring (egeg data below the LOD)data below the LOD) NonNon--homogeneous and outlying datahomogeneous and outlying data

99

9

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 10: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

SPECIFICSSPECIFICS of MATHEMATICAL GNOSTICSof MATHEMATICAL GNOSTICS

Theory ofTheory of individualindividual datadata andand smallsmall data samplesdata samples

RealisticRealistic assumptionsassumptionsUncertaintyUncertainty a lack of knowledgea lack of knowledgeldquoLet data speakldquoLet data speak for themsfor themseelveslvesrdquordquoResultsResults maximizing informatmaximizing informationionNaturalNatural robustnessrobustness

1010

10

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 11: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

1111

Comparison of two approachesComparison of two approaches

1111

11

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 12: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

GNOSTICGNOSTICDISTRIBUTION FUNCTIONSDISTRIBUTION FUNCTIONS

No a priori modelNo a priori model (e( verything from data)everything from data)

MaximumMaximum informationinformation

RobustnessRobustness in estimation of probabilityin estimation of probability

quantilesquantiles scale and location parameters scale and location parameters

bounds of data support and membershipbounds of data support and membership

intervalinterval

frac34frac34 RobustRobust correlationscorrelations 1212

12

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

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atio

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gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 13: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

GNOSTICGNOSTICDISTRIBUTION FUNCTIONS IIDISTRIBUTION FUNCTIONS II

DataData homogeneityhomogeneity teststests

MarginalMarginal cluster analysiscluster analysis

CrossCross--sectionsection filteringfiltering

Applicability toApplicability to censoredcensored datadata

Applicability toApplicability to heteroscedasticheteroscedastic datadata

1313

13

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 14: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

QUALITY OF METHODSQUALITY OF METHODSTO BE COMPAREDTO BE COMPARED

Relative sensitivity (Relative sensitivity (tresholdtreshold range) range)Homogeneity of resultsHomogeneity of resultsConsistency of resultsConsistency of results Internal (of methodrsquos own results)Internal (of methodrsquos own results) External (mutual consistency of methExternal (mutual consistency of met ods)hods)

InformativInformati enessveness of resultsof resultsPrecissionPrecission

1414

14

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 15: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

RELATIVE SENSITIVITYRELATIVE SENSITIVITY

Methodrsquos relative sensitivity dependsMethodrsquos relative sensitivity dependsOn the pollutantrsquos concentrationOn the pollutantrsquos concentrationOn the methodrsquos measuring domainOn the methodrsquos measuring domain

RS = (1RS = (1 ndashndash NCN) x 100 ()NCN) x 100 ()NCNC hellip number of data in the intervhellip number of data in th ale interval[sensitivity threshold[sensitivity threshold max(rangemax(range)])]

NN hellip all data of the sahellip all data of the s mpleample1515

15

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

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27

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28

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29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 16: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

HOMOGENIZATIONHOMOGENIZATIONTO BE OR NOT TO BETO BE OR NOT TO BE

Homogeneous dataHomogeneous datathe samethe same originorigin of true valuesof true valuesthe same nature of thethe same nature of the uncertaintyuncertainty

To homogenizeTo homogenize ProsPros

More certain main clusterMore certain main cluster ConsCons

Possible loss of informationPossible loss of informationRule homogenize and verifyRule homogenize and verify

1616

16

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

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2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

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27

2727

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28

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EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 17: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

MEASURABILITYMEASURABILITY

Homogenization hellip elimination of outliersHomogenization hellip elimination of outliersMeasMeas = (1= (1 ndashndash (NL+NU)N) x 100 ()(NL+NU)N) x 100 ()NL hellipNL hellip number of lower outliersnumber of lower outliersNU hellipNU hellip number of upper outliersnumber of upper outliersN hellipN hellip number of the samplersquos datanumber of the samplersquos dataNN ndashndash NLNL ndashndash NU hellipNU hellip data of the main clusterdata of the main cluster

1717

17

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

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27

2727

2828

28

2828

2929

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2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 18: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

1818

METHODS OF ANALYSISMETHODS OF ANALYSIS

GEOMETRYGEOMETRY(angles between vectors)(angles between vectors)

STATISTICSSTATISTICS(robust correlations)(robust correlations)

MATHEMATICAL GNOSTICS MATHEMATICAL GNOSTICS (robust correlations robust(robust correlations robustdistribution functions information distribution functions information and entropy of small data samples)and entropy of small data samples)

Dec Log (concentration) ugsampling system

1818

18

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 19: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

1919

Dec Log (concentration) ugsampling system

1919

19

2020

Co

nce

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yste

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2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

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2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 20: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

2020

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2020

20

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

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atio

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am

plin

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2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 21: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

DIFFERENCES IN METHODSDIFFERENCES IN METHODS

Different accumulation of pollutantsDifferent accumulation of pollutantsbullbull different mean concentrationsdifferent mean concentrationsbullbull differentdifferent variabilitiesvariabilities

Different relations between meansDifferent relations between means Rare exception agreement in PCB118Rare exception agreement in PCB118 Impact of outliers to SPMDImpact of outliers to SPMD NONO

2121

21

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 22: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

METHODrsquoS CONSISTENCYMETHODrsquoS CONSISTENCY

Methods areMethods are consistentconsistent when they givewhen they givesimilar resultssimilar results

Measuring of similarityMeasuring of similarityCorrelations or (more generally)Correlations or (more generally)

mean angles between vectors of resultsmean angles between vectors of resultsSIMccSIMcc = 100 x= 100 x correlcoefficientcorrelcoefficient ()()SIMqaSIMqa = 100 x (1= 100 x (1 ndashndash |Ang|180) ()|Ang|180) ()

2222

22

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 23: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

GNOSTIC CORRELATIONSGNOSTIC CORRELATIONS

Data error inData error in gnosticgnostic irrelevanceirrelevanceirir = (2p= (2p -- 1)21)2

pp hellip probability of the data itemhellip probability of the data itemCorrelation coefficient of two samplesCorrelation coefficient of two samples

Gcc(MNGcc(MN) =) = ccir(m)ir(nccir(m)ir(n))(m in M n in N) cc (m in M n in N) cc statiststatist corcoefcorcoef

RobustnessRobustness-- 1 lt=1 lt= irir lt= + 1lt= + 1 2323

23

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

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27

2727

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28

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nce

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atio

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am

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29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 24: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

SIGNIFICANCESIGNIFICANCE OF CORRELATIONSOF CORRELATIONS

Problems false statistical modelProblems false statistical model (normality finite data support)(normality finite data support) small data samplessmall data samples unrobustnessunrobustness

Gnostic estimating of significanceGnostic estimating of significancefrac34frac34 fast auxiliaryfast auxiliary usinusi g Spearmanrsquosng Spearmanrsquos

robust estimate of significancerobust estimate of significancefrac34frac34 carefullycarefully distribution function ofdistribution function of

correlation coefficientscorrelation coefficients2424

24

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

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27

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28

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29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 25: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

2525

25

2525

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

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am

plin

g s

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m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 26: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

QUANTILE VECTORSQUANTILE VECTORS

Make samplersquos distribution functionMake samplersquos distribution function Set a series of probabilitiesSet a series of probabilities p1hellipp1hellippNpN FindFind quantilesquantiles q1hellipq1hellipqNqN so thatso that PqkPqk==pkpk TakeTake q1hellipq1hellipqNqN as aas a quantilequantile vectorvectorAdvantagesAdvantages

Robustness making use of censored dataRobustness making use of censored dataindependence of data amount and ofindependence of data amount and of mean data value filtering effectmean data value filtering effect

2626

26

2727

27

2727

2828

28

2828

2929

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nce

ntr

atio

n u

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am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 27: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

2727

27

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2828

28

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Co

nce

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EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 28: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

2828

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nce

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EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

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2929

Co

nce

ntr

atio

n u

gs

am

plin

g s

yste

m

2929

29

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 30: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

EXTERNAL CONSISTENCYEXTERNAL CONSISTENCY

ApproachesApproaches CorrelationsCorrelations Angles betwAngl een MDes between MD--vectors of meansvectors of means Angles betweenAngles between quantilequantile vectovect rsro s Conjunction of typical data intervalsConjunction of typical data intervals Conjunction of data supportsConjunction of data supports

3030

30

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 31: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

INTERVAL ANALYSISINTERVAL ANALYSIS

1)1) Distribution functionsDistribution functions2)2) Interval analysisInterval analysis

a)a) Data supportData support (LB UB)(LB UB)b)b) Membership intervalMembership interval (LSB USB)(LSB USB)c)c) Interval of typical dataInterval of typical data (ZL UL)(ZL UL)d)d) Tolerance intervalTolerance interval (Z0L Z0U)(Z0L Z0U)

3)3) OverlappingOverlapping 100xconjunction(I1 I2)union(I1I2) ()100xconjunction(I1 I2)union(I1I2) ()

3131

31

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 32: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

INFORMATIVENESSINFORMATIVENESS

1)1) Data sampleData sample2)2) Distribution functionDistribution function3)3) ProbabilityProbability pp of an individual data itemof an individual data item4)4) Information of the data itemInformation of the data item

Info=(pInfo=(p log(plog(p) + (1) + (1--p)log(1p)log(1--p))logp (12)())log 12)5)5) InformativenessInformativeness of a data sampleof a data sample

100 x100 x MeM an(Infoean(Info) ()) ()3232

32

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 33: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

3333

EVALUATIONEVALUATION OF PRECISIONOF PRECISION

Weak variabilityWeak variability PrecPrec = 100 x (1= 100 x (1 ndashndash STDAVG) ()STDAVG) ()

((STDSTD hellip standard deviationhellip standard deviation AVGAVG helliphellip mean)mean)

Strong uncertaintyStrong uncertaintyPrecPrec = 100 x (1= 100 x (1 -- Mean(GWMean(GW) ) ()) ) ()

((GWGW helliphellip gnosticgnostic weight of data entropyweight of data entropy change caused by the uncertainty)change caused by the uncertainty)

0 lt= GW lt= 10 lt= GW lt= 1

33

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 34: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

SUMMARY COMPARISONSUMMARY COMPARISON

AverigeAverige of 14 evof 14 evaluationsaluations

MethodMethod NonNon--homdatahomdata HomogHomog data data

BentosBentos 609 609 627 627

DreissenaDreissena 645 645 675 675

PlantsPlants 642 642 689 689

SPMDSPMD 675 675 695 695

3434

34

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 35: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

3535

35

3535

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 36: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

RATINGRATIN OF METHODSG OF METHODS

FeatureFeature BentosBentos DreissDreiss PlantsPlants SPMDSPMDExtconsistencyExtconsistency 44 33 11 22IntconsistencyIntconsistency 44 33 22 11InformativenessInformativeness 11 33 44 22PrecissioPrecissionn 33 11 44 22HomogeHomogeneityneity 22 44 33 11RelsensitivityRelsensitivity 33 11 22 11Mean ratingMean rating 2828 2525 2727 1515

3636

36

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

3737

37

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

3838

38

3939

hellip thank you for your attention

PCDDF

39

Page 37: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

ndash

ndash

ndash

ConclusionsConclusions

Passive sampling like SPMDs shown the bestPassive sampling like SPMDs shown the best results if there are no legal requirements for biotaresults if there are no legal requirements for biota biotic organisms can be replacedbiotic organisms can be replaced

Do not forget to analyze data preciselyDo not forget to analyze data precisely independently before your interpretationindependently before your interpretationndash Do not rely ONLY on functionality of any processingDo not rely ONLY on functionality of any processing

packagepackagendash Statistical approach has some limitations on small dataStatistical approach has some limitations on small data

sets (majority of monitoring studies)sets (majority of monitoring studies)

Any headache from analytical tools can beAny headache from analytical tools can be eliminated by expeeliminated by exp rienceeriencendash Try itTry it

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Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

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Page 38: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

Further intentionsFurther intentions

Finalization of Gnostic analytical toolFinalization of Gnostic analytical tool with GUI (Swith GUI (S--Plus)Plus)

Extension to other platExtension to other platforms byforms by interfaceinterface

Linking to databases (LIMS GIS hellip)Linking to databases (LIMS GIS hellip) Training and disseminationTraining and dissemination Projects solutions and participationsProjects solutions and participations

ndashndash Join us 2Join us 2--FUN projectFUN project www2www2--funorgfunorg

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hellip thank you for your attention

PCDDF

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Page 39: COMPARISON OF SPMDs AND BIOTIC SAMPLERS … BIOTIC SAMPLERS USING GNOSTIC ANALYSIS ... GEOMETRY (angles between ... Finalization of Gnostic analytical tool,Finalization of Gnostic

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