www.chrisbilder.com1 of 36 turning data into knowledge to solve real world problems christopher r....

www.chrisbilder.com 1 of 36

Turning data into knowledge to Turning data into knowledge to solve real world problemssolve real world problems

Christopher R. Bilder, Ph.D.Department of Statistics

University of Nebraska-Lincolnwww.chrisbilder.com


11 years ago…11 years ago… The year is 1993 Pearl Jam records second CD, Vs.,

– Daughter, Go, Elderly Woman Behind the Counter in a Small Town

– Almost 1 million CDs are sold in the first week

Bill Clinton was inaugurated as the 41st president Movies

– Jurassic Park

– Schindler's List

– Sleepless in Seattle

Husker football – Began 1993 by losing the Orange Bowl badly (again)

– 1993 season went undefeated

Math 4750 - Introduction to Probability and Statistics II – 4-5:15PM Tuesdays and Thursdays in DC 164

– Dr. Stephens


11 years ago…11 years ago… Actuarial Science!

– Planned to be an actuary when I started college– Internship at National Indemnity Company at 32nd and Harney – Passed 4 exams under old system

Wanted to go on to graduate school– Math?– Actuarial Science?

Hypothesis testing in Math 4750– Use for decision making!– Scientifically prove a hypothesis or statement – Go to graduate school for statistics!

1994 received BS in Mathematics with pre-actuarial science minor from UNO


After UNOAfter UNO Went on to graduate school for statistics

– MS 1996 from Kansas State University– PhD 2000 from Kansas State University– Internships at INEEL in Idaho and pharmaceutical company in Kansas

City– Consult with students and professors in

• Institute of Social and Behavorial Research• College of Agriculture

– Taught courses like Statistical Methods I and II (STAT 3000 and 3010)

Assistant Professor at Oklahoma State University– Department of Statistics – 2000-2003

Assistant Professor at UNL– NEW Department of Statistics– 2003-present


PurposePurpose Tell you a little about statistics

– Statistics is mainly a graduate discipline– Most statisticians have undergraduate degrees in math

Turning data into knowledge to solve real world problems– 3 actual examples that come from my teaching and research

About statistics at UNL Website (www.chrisbilder.com/statistics) for more information


Undergraduate teaching example for a course like STAT 3000 How could you determine which grocery store, Super Wal-

Mart or Albertson’s, has lower average prices?

– Paired or dependent two sample hypothesis test for Wal-Mart - Albertsons

– Sample the same items at each store

Grocery store pricesGrocery store prices


Undergraduate teaching example for a course like STAT 3000 How could you determine which grocery store, Dillon’s or

Food-4-Less in Manhattan, KS, has lower average prices?

– Paired or dependent two sample hypothesis test for Dillon’s - Food-4-Less

– Sample the same items at each store

Only cereals from Fall 1998– Possible problems described later

Grocery store pricesGrocery store prices


Grocery store pricesGrocery store prices Sample:

Item Dillon's Food-4-Less Difference1 Malt-o-meal - Tootie Fruities, 15oz $1.99 $1.84 $0.152 Malt-o-meal - Golden Puffs, 18oz $1.99 $1.84 $0.153 Quaker Oats - Life Cereal: Original, 21oz $3.69 $3.49 $0.204 Cheerios, 20oz $4.59 $4.24 $0.355 Cheerios, 15oz $3.79 $3.50 $0.296 Wheaties, 18oz $3.89 $3.60 $0.297 Kellogg’s Funpack, 8 9/16oz $2.89 $2.67 $0.228 Kellogg’s Variety Pack 9 5/8oz. $3.49 $3.14 $0.359 Kellogg’s Frosted Mini-Wheats Bite Size

19oz$3.49 $2.50 $0.99

10 Kellogg’s Frosted Mini-Wheats, 16oz $2.50 $2.73 -$0.2311 Kellogg’s Frosted Flakes, 15oz $3.19 $2.92 $0.2712 Our Family Frosted Flakes, 20oz. $2.50 $1.90 $0.6013 Kellogg’s Crispix, 12oz. $3.49 $3.20 $0.2914 Our Family - Raisin Bran, 20oz $2.50 $1.92 $0.5815 Kellogg’s Smart Start, 13.3oz $3.49 $3.24 $0.2516 Grape Nuts, 24oz $3.00 $2.85 $0.1517 Frosted Alpha Bits, 15oz $3.00 $2.87 $0.13


Grocery store pricesGrocery store prices Do you think there are

mean differences?Item Dillon's Food-4-Less Difference

1 Malt-o-meal - Tootie Fruities, 15oz $1.99 $1.84 $0.152 Malt-o-meal - Golden Puffs, 18oz $1.99 $1.84 $0.153 Quaker Oats - Life Cereal: Original, 21oz $3.69 $3.49 $0.204 Cheerios, 20oz $4.59 $4.24 $0.355 Cheerios, 15oz $3.79 $3.50 $0.296 Wheaties, 18oz $3.89 $3.60 $0.297 Kellogg’s Funpack, 8 9/16oz $2.89 $2.67 $0.228 Kellogg’s Variety Pack 9 5/8oz. $3.49 $3.14 $0.359 Kellogg’s Frosted Mini-Wheats Bite Size

19oz$3.49 $2.50 $0.99

10 Kellogg’s Frosted Mini-Wheats, 16oz $2.50 $2.73 -$0.2311 Kellogg’s Frosted Flakes, 15oz $3.19 $2.92 $0.2712 Our Family Frosted Flakes, 20oz. $2.50 $1.90 $0.6013 Kellogg’s Crispix, 12oz. $3.49 $3.20 $0.2914 Our Family - Raisin Bran, 20oz $2.50 $1.92 $0.5815 Kellogg’s Smart Start, 13.3oz $3.49 $3.24 $0.2516 Grape Nuts, 24oz $3.00 $2.85 $0.1517 Frosted Alpha Bits, 15oz $3.00 $2.87 $0.13

25%

75%

50%


Grocery store pricesGrocery store prices Paired two sample hypothesis test

– Ho:Dillon’s - Food-4-Less=0Ha:Dillon’s - Food-4-Less0

– t = 4.77, p-value = 0.0002, 95% C.I.: 0.1644 < Dillon’s - Food-4-Less < 0.4274

– Reject equal mean prices

If price was the only consideration, what store should one shop at?

Assumptions– Prices and selection at these two stores are indicative of all stores– Normal populations– The sample was taken in 1998; what about now?– Finite populations


MS report – applying statistics or investigating new methodology– 120 page book!– Reduced version published in Chance in 1998

Find a model to estimate the probability of successfor placekicks in the NFL

Video– January 7, 1996– Playoff game– Indianapolis Colts 10

Kansas City Chiefs 7– Lin Elliott of KC will attempt

a 42 yard field goal to tie the game and send it into overtime

PlacekickingPlacekicking


PlacekickingPlacekicking What factors affect the probability of success for NFL

placekicks?– Distance– Pressure – How do you quantitatively measure?– Wind– Grass vs. artificial turf– Dome vs. outdoor stadium

Collected data >1,700 placekicks during the 1995 NFL season

Find the best logistic regression model of the form

where p is the probability of success xi for i=1,…,k are independent variables

i measures the effect of xi on p for i=1,…,k

0 1 1 2 2 k k

0 1 1 2 2 k k

x x x

x x x

ep=

1 e


PlacekickingPlacekicking The i’s are parameters which are estimated through

maximum likelihood estimation Estimated model

– Change: lead change = 1, non-lead change = 0– Distance: distance in yards– PAT: point after touchdown = 1, field goal = 0– Wind: windy (speed > 15 MPH) = 1, non-windy = 0

What is the estimated probability of success for Elliott’s field goal?– Conditions:– Estimated probability of success: – 90% confidence interval for probability of success:

0.6298 < p < 0.7402

Change Distance PAT Wind1 42 0 0

p 0.6850

4.4984 0.3306change 0.0807distance 1.2592PAT 2.8778wind 0.0907distance wind

4.4984 0.3306change 0.0807distance 1.2592PAT 2.8778wind 0.0907distance wind

ep=

1 e


Estimated probability of success for a field goal (PAT=0)

20 30 40 50 60

0.0

0.2

0.4

0.6

0.8

1.0

Distance in Yards

Est

ima

ted

Pro

ba

bili

ty o

f S

ucc

ess

Estimated probability of success of a field goal (PAT=0)

Change=0, Wind=0Change=1, Wind=0Change=0, Wind=1Change=1, Wind=1

42

0.685



20 30 40 50 60

0.0

0.2

0.4

0.6

0.8

1.0

Distance in Yards

Est

ima

ted

Pro

ba

bili

ty o

f S

ucc

ess


Lowest Number of Risk Factors

Estimated Probability90% Confidence Interval

Highest Number of Risk Factors

Estimated Probability90% Confidence Interval


PlacekickingPlacekicking UNL Department of Statistics developing statistics in sports

specialty – Dr. David Marx

• Works with the UNL athletic department• January 10, 2004 Omaha World Herald article about his work the

men’s basketball team (available at www.chrisbilder.com/statistics)• His students this semester have worked with NASCAR, Lincoln SE

women’s high school soccer team, and Tendu, Inc. (baseball software company).

– Myself• Placekicking• Modeling 64-team NCAA tournaments


HCV prevalenceHCV prevalence MS/PhD research – forwarding statistical theory and methodology Hepatitis C (HCV)

– Viral infection that causes cirrhosis and cancer of the liver

– Since HCV is transmitted through contact with infectious blood, screening blood donors is important to prevent further transmission

Questions:– How can blood be screened in a cost effective and timely manner?

– What proportion of people is inflicted with HCV in a population?

Individual testing– Each blood sample is tested individually

– Problems:

• Costly

• Time

+ or - + or - + or - + or - + or -+ or -


Group testing– Pool the blood samples together to form n groups of size s

– If the GROUP sample is negative, then all s people do not have the disease

– If the GROUP sample is positive, then at least ONE of the s people have the disease

• May want to determine who in the group has the disease– Strategy works well when prevalence of a disease is small– Dorfman (1943) – first used to test members of the military for disease

HCV prevalenceHCV prevalence

+ or - + or - + or -

Group 1 Group 2 Group n


HCV prevalenceHCV prevalence Notation

– Let p = probability an INDIVIDUAL is HCV positive– Let = probability a GROUP is HCV positive– Let s = group size– Let n = number of groups– Let T be a random variable denoting the number of positive GROUPS

• T has a binomial distribution with “n trials” and “ as the probability of success”

•

– Let Y be an UNOBSERVABLE random variable denoting the number of positive INDIVIDUALS in a group

• Y has a binomial distribution with “s trials” and “p as the probability of success”

•

t n tnf(t) (1 ) for t=0,1,2,...,n

t

s s ysg(y) p (1 p) for y=0,1,2,...,s

y


HCV prevalenceHCV prevalence How can we estimate p?

– We observe information about the groups, not individuals! – Maximum likelihood estimate of is = # positive / # of groups– = P(group is positive)

= P(at least one individual is positive)

= 1 – P(no individuals are positive) using complement rule

= 1 – (1-p)s since p = P(individual is positive) and s individuals per group

– Solve for p, p = 1- (1- )1/s

– Use invariance property of maximum likelihood estimates to find

• For fixed sample size, is positively biased• It is unbiased as n

ˆ T /n

1/ s 1/ sMLE

ˆp 1 (1 ) 1 (1 T /n) p


HCV prevalenceHCV prevalence Can we find a better estimator?

– Yes

How do we measure “better”?– Let be an estimator of – Bias =

• Which would you prefer for a bias: small or large• Given two estimators, which would you prefer

– Estimator with smaller bias– Estimator with larger bias

– Can compare to competing estimators through the “relative bias”• Let and be two estimators of

•

• If RB > 1, then and would be “better”

ˆE( )

1

2

ˆBias( )RB =

ˆBias( )

1 2

1 2ˆ ˆBias( ) Bias( ) 2


HCV prevalenceHCV prevalence New estimators

– Proposed in Tebbs, Bilder, and Moser (Communications in Statistics, 2003) and Bilder and Tebbs (under review in Biometrical Journal)

– Derived through “empirical Bayesian methods”

–

where

and is found from maximizing

–

1/ s

EB2t 1

p 1 1ˆn / s 1

EB1

ˆ ˆ(n / s 1) (n t / s 1/ s)p 1

ˆ ˆ(n t / s) (n / s 1 1/ s)

1 x

0

( ) x e dx

T(n 1) (n t / s)

f (t | )s (n t 1) (n / s)


0.00 0.02 0.04 0.06 0.08 0.10

05

1015

n=30 and s=10

p

Rel

ativ

e bi

as

EB1EB2EB3

0.00 0.02 0.04 0.06 0.08 0.10

0.6

0.7

0.8

0.9

1.0

1.1

1.2

n=30 and s=10

p

Rel

ativ

e ef

ficie

ncy

EB1EB2EB3

0.00 0.02 0.04 0.06 0.08 0.10

05

1015

n=80 and s=25

p

Rel

ativ

e bi

as

EB1EB2EB3

0.00 0.02 0.04 0.06 0.08 0.10

0.6

0.7

0.8

0.9

1.0

1.1

1.2

n=80 and s=25

p

Rel

ativ

e ef

ficie

ncy

EB1EB2EB3

0.00 0.02 0.04 0.06 0.08 0.10

05

1015

n=30 and s=10

p

Rel

ativ

e bi

as

EB1EB2EB3

0.00 0.02 0.04 0.06 0.08 0.10

0.6

0.7

0.8

0.9

1.0

1.1

1.2

n=30 and s=10

p

Rel

ativ

e ef

ficie

ncy

EB1EB2EB3

0.00 0.02 0.04 0.06 0.08 0.10

05

1015

n=80 and s=25

p

Rel

ativ

e bi

as

EB1EB2EB3

0.00 0.02 0.04 0.06 0.08 0.10

0.6

0.7

0.8

0.9

1.0

1.1

1.2

n=80 and s=25

p

Rel

ativ

e ef

ficie

ncy

EB1EB2EB3

MLE EB,iˆ ˆRB Bias(p ) /Bias(p ) ; when RB > 1, is better thanEB,ip MLEp

1n=30, s=10

n=80, s=25

1


HCV prevalenceHCV prevalence Estimation of HCV prevalence in Xuzhou City, China.

– Data from Liu et al. (Transfusion, 1997)– 1,875 blood donors screened for HCV at the Blood Transfusion Service

in Xuzhou City, China• There were 42 positive blood donors found

– In order to test the usefulness of group testing, blood samples were also pooled

• n = 375 groups• s = 5 individuals per group• t = 37 positive groups

– Point estimates of p, the individual probability of being HCV positive• Using individual data: 42/1875 = 0.0224• Using group data:

EB1p 0.020557MLEp 0.020562

EB2p 0.020534


HCV prevalenceHCV prevalence Multiple vector transfer designs

– Swallow (Phytopathology, 1985)– Want to estimate the probability a insect vector transfers a pathogen

(virus, bacteria, etc.) to a plant

Brown planthopper

Whitebacked planthopper


HCV prevalenceHCV prevalence Multiple vector transfer designs (continued)

– s insect vectors are transferred to a healthy plant– The plant is the “group”– Observe number of plants which contract the pathogen

Greenhouse

Enclosed test plant

Does not transmit virus

Transmits virus

y=0

y=1y=0

y=1y=0

y=0Planthoppery =0 if plant is negative, 0 if plant is positive


HCV prevalenceHCV prevalence New research

– Include independent variables to help model p in a logistic regression model,

– Problem: Do not have the individual outcomes– Help to decide who to retest if get a positive group– Multiple traits

• HCV• HIV• Other disease• Simultaneously model

0 1 1 2 2 k k

0 1 1 2 2 k k

x x x

x x x

ep=

1 e


Why statistics?Why statistics? Statistics is used in many diverse areas!

– Statistics is the “science of science”– Florence Nightingale quote:

the most important science in the whole world: for upon it depends the practical application of every other science and of every art: the one science essential to all political and social administration, all education, all organization based on experience, for it only gives results of our experience.

I hope you have an interest to take more statistics courses – UNO– Graduate school in statistics or non-statistics programs

Of course, I want you to consider coming to UNL!


Statistics at UNLStatistics at UNL Facts

– July 1, 2003 formed– 11 faculty + 2 more in 2004– No undergraduate major– 40+ graduate students (most MS)– Strong commitment from administration– Hardin Hall on East Campus


Statistics at UNLStatistics at UNL

33rd s

t.

Department of Statistics


Statistics at UNLStatistics at UNL Background of new students

– A few statistics courses – like UNO MATH 4740 and 4750– Statistics is mainly a graduate discipline– Majority have math degrees

Recommendation for UNO classes– Math 4740 and 4750 Intro. to Probability and Statistics I and II – Math 3300 Numerical Methods – Math 4760 Topics in Modeling– Math 4050 Linear Algebra– Math 4230 and 4240 Mathematical Analysis I and II

• Helpful if you plan to go on for a PhD– Stat 3000 and 3010 Statistical Methods I and II


Statistics at UNLStatistics at UNL Recommendation for UNO classes (continued)

– Business administration course: 3140 Business Statistical Applications – Computer science programming courses– Information Systems & Quantative Analysis Department courses

• 4150 Advanced Statistical Methods for IS&T• 8160 Applied Distribution Free Statistics • 8340 Applied Regression Analysis• 9120 Applied Experimental Design and Analysis• 9130 Applied Multivariate Analysis


Statistics at UNLStatistics at UNL Assistantships

– Work 16-20 hours a week– Teaching - $13K per school year + tuition (MS students)– Project Fulcrum grants - $30K per school year!

• 6 statistics students over the past 3 years have received grant– Research - variable depending on grants

• Statistics and non-statistics faculty grants

What makes us unique?– Consulting course and help desk– STAT 971 – Statistical Modeling– Statistics in sports and work with UNL athletic department– Consulting - All departments in the College of Agriculture and Natural

Resources – Gallup– Bioinformatics


Statistics at UNLStatistics at UNL Where do statistics graduates work?

– Pharmaceutical – Pfizer, Merck – Marketing – Target, Hallmark– Government research labs – INEEL, Los Alamos, Sandia, Argonne– Agriculture - Pioneer Hi-Bred – Consulting firms – Quintiles– Everyone that I have known has had a job offer before they graduated!

Salaries– Non-academic starting (2003 American Statistical Association survey)

– Survey response rate was 23.5% by organizations surveyed– See salary surveys at the American Statistical Association’s website

Degree Sample size 25th 50th 75th

MS 102 45.5K 50K 59KPhD 99 60K 65K 75K

Percentile


Statistics at UNLStatistics at UNL Applying for graduate school in statistics

– Send out applications before end of fall semester– Apply to more than one school – Visit schools in fall or early spring– Assistantship offers usually first go out in March

7th Annual UNL Regional Workshop in Mathematical Sciences– Statistics, Mathematics, and Computer Science departments– November 2004– Friday afternoon & evening and Saturday morning– Speakers introducing statistics and jobs in statistics– FUNDING available!


Statistics at UNLStatistics at UNL For more information…

– E-mail me at [email protected] or [email protected] • Advice• Sit in on a class

– Website: www.chrisbilder.com/statistics • This PowerPoint presentation• Links to

– Introductory information about being a statistician– Jobs (including internships)– Salary information– List of all Departments of Statistics– Professional societies – MS and PhD course websites that myself and others teach– Newspaper and magazine articles about statistical applications

www.chrisbilder.com1 of 36 turning data into knowledge to solve real world problems christopher r....

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