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the
flight mh370& bayes theoryMasilamani Ramasamy
- a scientific management expert([email protected])
Masilamani RamasamyConsultant Trainer
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MH370 tracking
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Bayes' Theorem
also called, Bayes' lawor Bayes' rule based on probability theory,
mathematics and Statistics
named after Thomas Bayes(/bez/17011761)
Bayes suggested the theorem toupdate beliefs
Significantly edited and updated byRichard Price
Bayes' theorem is to the theory ofprobability what Pythagoras'stheoremis to geometry-HaroldJeffreys
http://en.wikipedia.org/wiki/Thomas_Bayeshttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Richard_Pricehttp://en.wikipedia.org/wiki/Richard_Pricehttp://en.wikipedia.org/wiki/Pythagorean_theoremhttp://en.wikipedia.org/wiki/Pythagorean_theoremhttp://en.wikipedia.org/wiki/Pythagorean_theoremhttp://en.wikipedia.org/wiki/Pythagorean_theoremhttp://en.wikipedia.org/wiki/Pythagorean_theoremhttp://en.wikipedia.org/wiki/Pythagorean_theoremhttp://en.wikipedia.org/wiki/Richard_Pricehttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Thomas_Bayes -
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probability theory
rooted in,
the science ofStatistics
the science ofMathematics
the probability of anevent occurring
the analysis ofrandom phenomena
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statistical theory
gives, ways of comparing
statisticalprocedures
a best possibleprocedure forstatistical problems
guidance on thechoice betweenalternative
procedures
Passenger Identities Number
China/Taiwan 154
Malaysia 38
India 5
Indonesia 7
Australia 6
France 4
USA 3
New Zealand 2
Canada 2
Russia 1
Italy 1
Netherlands 1
Austria 1
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statistical theory
covers
Statistical decisionmethods and problems
Statistical inferences orconclusions
actions and deductions
To satisfy the basic principlesstated for these differentapproaches.
STATISTICS(FACTS)
Aircraft: Malaysian Air Lines
Aircraft Age: 11years 10
months
Aircraft Type: Boeing 777 ERFlight No: MH370(shared with
China Southern Airlines)
Passengers travelled: 227
Crew Travelled: 12
Nationalities: 14Take Off Time: 12.41 am
From: Kuala Lumpur, Malaysia
To: Beijing, China
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Statistics
is the study of thecollection, organization,analysis, interpretation and
presentation of informationor data
all aspects of data includingthe planning of data
collection in terms of thedesign of surveys andexperiments are used
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mathematical roots
Two mathematical results of Bayes Theorem
are,
THE LAW OF LARGE NUMBERS, and
THE CENTRAL LIMIT THEOREM
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law of large numbers(LLN)
Is a theorem
describes the result ofperforming the same
experiment a largenumber of times
thus the average of resultsobtained should be close
to the expected value, and The result will tend to
become closer to reality
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central limit theorem(CLT)
the arithmetic mean of asufficiently large number ofiterates of independent
random variables, each with awell-defined expected valueand well-defined variance,will be approximately
normally distributed This will probably lead to a
conclusion of the reality
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normal distribution
suppose sample contains a large number of
observations,
each observation being randomlygenerated,
in a way that does not depend on the
values of the other observations that the arithmetic average of the
observed values is computed,
and if this procedure is performedmany times,
then central limit theorem says the
computed values of the average will bea normal distribution
The normal distribution is commonlyknown as a "bell curve"
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Bayes' theorem
is,
a result that is of importancein the mathematical
manipulation of conditionalprobabilities
It is a result that derives fromthe more basic axioms of
probability It is a result that can lead to
realistic conclusions
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Bayesian (or epistemological)
interpretation probability measures a degree of belief
Bayes' theorem then links the degree ofbelief
in a proposition before and after
accounting for evidence. example, take a proposal that a biased
coin is twice as likely to land heads than tails.
Degree of belief in this might initially be50%.
The coin is then flipped a number oftimes to collect evidence.
Belief may rise to 70% if the evidencesupports the proposition
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axioms of probability
probability is,
a game of chance
measures the real, physical tendency of
something to occur
Measures how strongly one believes it will occur
draws on both these elements?
interprets the probability values of probability
theory to answer the above questions
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real life probabilityEvent Or Occurrence Non-Random event Random Event
Weather Seasonal Change, Local
Climate
Precipitation, Temperature on
Specific Days
Car Accidents Safe or Unsafe Driving
Practices
Specific Cars or Conditions
Met on the Road
Customers at Mall Hours Open, Time of the Day Specific Pattern of CustomerArrival
State Lottery Decision About Games
Available, Prices and Awards
Numbers Drawn or Winning
Patterns on Tickets
Plane Crash Ability of Flight Captains,
Security Measures
Plane Engine Failure,
Terrorists Intrusion
Student Grades Amount of Time of study,
Revision and Class
Preparation
Appearance of Specific
questions on Tests
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the search
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why MH370 flight missing?
Its loss is a mystery
Many theories, probabilitiesand interpretations stillremain
Inconclusive, inadequateand intriguing
Probably Bayes Theoreticalapproach would help
Scientists tend to believe inthis theory as a probablelead to discovery of themissing plane
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the theory that would not die
Its a very short,simple equation thatsays you can start out
with hypothesisabout something -and it doesnt matterhow good thehypothesis is,
- Sharon Bertsch McGrayne
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how
because of,
this character of the
formula
forcing researchers to
change their hypothesis
with each new information
that the probability
becomes more accurate
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the proof Bayes Theorem allows the
organisation of available data withassociated uncertainties andcomputation of the PDF
Scientists applied Bayes Theorem inthe Air France incident of 2009
French scientist Pierre Simon Laplace,helped locate German U-boats duringWorld War II and spot Sovietsubmarines during the Cold War
More recently, it is used in Google's"driverless cars" project and in stockmarket predictions
PDF or the probability distributionfunction, identified the targetlocation given these data"
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Why Not?
Advocates of this theory said itwas also used in the search for theblack box of the ill-fated Air Franceflight 447, which crashed in thevast Atlantic Ocean in June 2009
What took two years for otherexperts in the search for the blackbox, took only five days forconsultants who applied the BayesTheorem, to finally find the device12,000 feet under water.
In the current search for flightMH370, it is highly unlikely thatBayes Theorem is being applied.
Air France Accident summary
Date 1 June 2009
Summary Entered high altitude stall,
impacted ocean
Site Atlantic Ocean
near waypointTASIL[1]
30357N303342WCoordinat
es: 30357N303342WPassengers 216
Crew 12
Fatalities 228 (all)
Survivors 0
Aircraft type Airbus A330-203
Operator Air France
Registration F-GZCP
Flight origin Rio de JaneiroGaleo Airport
Destination Paris-Charles de Gaulle Airport
http://en.wikipedia.org/wiki/Atlantic_Oceanhttp://en.wikipedia.org/wiki/Waypointhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://en.wikipedia.org/wiki/Geographic_coordinate_systemhttp://en.wikipedia.org/wiki/Geographic_coordinate_systemhttp://en.wikipedia.org/wiki/Geographic_coordinate_systemhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://en.wikipedia.org/wiki/Airbus_A330http://en.wikipedia.org/wiki/Air_Francehttp://en.wikipedia.org/wiki/Aircraft_registrationhttp://en.wikipedia.org/wiki/Rio_de_Janeiro%E2%80%93Gale%C3%A3o_International_Airporthttp://en.wikipedia.org/wiki/Paris-Charles_de_Gaulle_Airporthttp://en.wikipedia.org/wiki/Paris-Charles_de_Gaulle_Airporthttp://en.wikipedia.org/wiki/Paris-Charles_de_Gaulle_Airporthttp://en.wikipedia.org/wiki/Rio_de_Janeiro%E2%80%93Gale%C3%A3o_International_Airporthttp://en.wikipedia.org/wiki/Rio_de_Janeiro%E2%80%93Gale%C3%A3o_International_Airporthttp://en.wikipedia.org/wiki/Rio_de_Janeiro%E2%80%93Gale%C3%A3o_International_Airporthttp://en.wikipedia.org/wiki/Aircraft_registrationhttp://en.wikipedia.org/wiki/Air_Francehttp://en.wikipedia.org/wiki/Airbus_A330http://en.wikipedia.org/wiki/Airbus_A330http://en.wikipedia.org/wiki/Airbus_A330http://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://en.wikipedia.org/wiki/Geographic_coordinate_systemhttp://en.wikipedia.org/wiki/Geographic_coordinate_systemhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://tools.wmflabs.org/geohack/geohack.php?pagename=Air_France_Flight_447¶ms=3_03_57_N_30_33_42_W_type:eventhttp://en.wikipedia.org/wiki/Air_France_Flight_447http://en.wikipedia.org/wiki/Waypointhttp://en.wikipedia.org/wiki/Atlantic_Oceanhttp://en.wikipedia.org/wiki/Stall_(flight) -
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Inconclusive Theories about MH 370
Sudden shut down of allflight systems
Sabotage by suspects
Hijackers on board
Undesirable clients in thecockpit
Deep dive into ocean bed
Disgruntled or insane flight
officer Ill equipped management
and security systems
Etc., etc., etc..
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learn from experience
Bayes' Theorem,
is all about learningfrom experience
one would need"reasonably accuratepast experiences" forthe theorem to work
in other words, tocalculate accurately tolocate the plane
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find the plane
go find theplane, withscience in your
bag, enough ofspiritual andemotional
beliefs andtraditionalmethods-masi
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thanks
Malaysian government reports/statements
Wikipedia.com
Malaysiakini Radio/TV and the Media
Photo Gallery
Gayesian experts like Sharon Bertsch McGrayne