MH 370 & the Bayes theory

Flight MH370 & The Bayes Theory

By Masilamani Ramasamy

Leadership & Scientific Management Consultant([email protected])

MH370

Bayes' Theorem

• also called, Bayes' law or Bayes' rule• based on probability theory,

mathematics and Statistics• named after Thomas Bayes (/ˈbeɪz/;

1701–1761) • Bayes suggested the theorem to

update beliefs• Significantly edited and updated by

Richard Price• Bayes' theorem “is to the theory of

probability what Pythagoras's theorem is to geometry” -Harold Jeffreys

probability theory

rooted in, • the science of Statistics• the science of

Mathematics• the probability of an

event occurring• the analysis of random

phenomena

statistical theory

gives, – ways of comparing

statistical procedures– a best possible

procedure for statistical problems

– guidance on the choice between alternative procedures

Passenger Identities China/Taiwan 154Malaysia 38India 5Indonesia 7Australia 6France 4USA 3New Zealand 2Ukraine 2Canada 2Russia 1 Italy 1 Netherlands 1Austria 1

statistical theory

covers – Statistical decision

methods and problems– Statistical inferences or

conclusions– actions and deductions

To satisfy the basic principles stated for these different approaches.

Statistics(facts)Aircraft: Malaysian Air LinesAircraft Age: 11years 10 monthsAircraft Type: Boeing 777 ERFlight No: MH370(shared with China Southern Airlines)Passengers travelled: 227Crew Travelled: 12Nationalities: 14Take Off Time: 12.41 amFrom: Kuala Lumpur, MalaysiaTo: Beijing, China

Statistics

• is the study of the collection, organization, analysis, interpretation and presentation of information or data

• all aspects of data including the planning of data collection in terms of the design of surveys and experiments are used

mathematical roots

• Two mathematical results of Bayes Theorem are,–THE LAW OF LARGE NUMBERS, and –THE CENTRAL LIMIT THEOREM

law of large numbers (LLN)

• Is a theorem• describes the result of

performing the same experiment a large number of times

• thus the average of results obtained should be close to the expected value, and

• The result will tend to become closer to reality

central limit theorem (CLT)

• the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed

• This will probably lead to a conclusion of the reality

normal distribution• suppose

– sample contains a large number of observations, – each observation being randomly generated,– 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 performed many times, – then central limit theorem says the computed

values of the average will be a “normal distribution“

– The normal distribution is commonly known as a "bell curve"

bayes' theorem

is, • a result that is of importance in

the mathematical manipulation of conditional probabilities

• It is a result that derives from the more basic axioms of probability

• It is a result that can lead to realistic conclusions

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

EVENT or OCCURENCE

NON-RANDOM EVENT RANDOM EVENT

Weather Seasonal change, Local climate

precipitation, temperature onspecific 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 customer arrival

State lottery Decision about games available, prices & awards

numbers drawn or winningpatterns on tickets

Plain crash Ability of flight captains, security measures

Plane engine failure, terrerists intrusion

Student grades Amount of study, revision and class preparation

appearance of specific questions on tests

Real Life Probability

why MH370 flight missing?• Its loss is a mystery• Many theories, probabilities and interpretations still remain• Inconclusive, inadequate and intriguing• Probably Bayes Theoretical approach would help• Scientists tend to believe in this Theory as a probably lead

to discovery of the missing plane

the theory that would not die

• “It’s a very short, simple equation that says you can start out with hypothesis about something - and it doesn’t matter how good the hypothesis is,”

• - Sharon Bertsch McGrayne

how

because of,• this character of the formula• forcing researchers to change

their hypothesis with each new information

• that the probability becomes more accurate

the proof

• Bayes’ Theorem “allows the organisation of available data with associated uncertainties and computation of the PDF

• Scientists applied Bayes’ Theorem in the Air France incident of 2009

• French scientist Pierre Simon Laplace, helped locate German U-boats during World War II and spot Soviet submarines during the Cold War

• More recently, it is used in Google's "driverless cars" project and in stock market predictions

• PDF or the probability distribution function, identified the target location given these data".

Why Not?• Advocates of this theory said it was also used in the search for the

black box of the ill-fated Air France flight 447, which crashed in the vast Atlantic Ocean in June 2009.

• What took two years for other experts in the search for the black box, took only five days for consultants who applied the Bayes’ Theorem, to finally find the device 12,000 feet under water.

• In the current search for flight MH370, it is “highly unlikely” that Bayes’ Theorem is being applied.

black box

Inconclusive Theories about MH 370

• Sudden shut down of all flight systems• Smoke or fire alarm• Sabotage by suspects• Hijackers on board• ‘Undesirable clients’ in the cockpit• Deep dive into ocean bed• Disgruntled or insane flight officer• Ill equipped management and security systems• Incapable flight officers• Etc., etc., etc…..

learn from experience

• Bayes' Theorem, – is all about learning from

experience–one would need

"reasonably accurate past experiences" for the theorem to work– in other words, to

calculate accurately to locate the plane

find the plane

•go find the plane, with science in your bag, enough of spiritual beliefs, emotional reasoning and traditional methods

Thanks

• Malaysian Airlines• Wikipedia• Malaysiakini• Google.com• Professionals