the flight

MH370 & Bayes theory

Masilamani Ramasamy- a scientific management expert

(misilamani@yahoo.com)

Masilamani RamasamyConsultant Trainer

MH370 tracking

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 theorygives, –ways of comparing

statistical procedures– a best possible

procedure for statistical problems– guidance on the

choice between alternative procedures

Passenger Identities Number

China/Taiwan 154

Malaysia 38India 5

Indonesia 7

Australia 6

France 4

USA 3

New Zealand 2

Canada 2

Russia 1

Italy 1

Netherlands 1

Austria 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

Bayesian (or epistemological) interpretation

• probability measures a degree of belief• Bayes' theorem then links the degree of belief • 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 be

50%. – The coin is then flipped a number of

times to collect evidence.– Belief may rise to 70% if the evidence

supports the proposition

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

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 Customer Arrival

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

the search

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 probable 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.

Air France Accident summaryDate 1 June 2009Summary Entered high altitude stall,

impacted ocean

Site Atlantic Oceannear waypoint TASIL [1]

3°03 57″N 30°33 42″W′ ′Coordinates: 3°03 57″N 30°33 42″W′ ′

Passengers 216Crew 12Fatalities 228 (all)Survivors 0Aircraft type Airbus A330-203Operator Air FranceRegistration F-GZCPFlight origin Rio de Janeiro–Galeão Airport

Destination Paris-Charles de Gaulle Airport

Inconclusive Theories about MH 370

• Sudden shut down of all flight systems

• 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• 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 and emotional beliefs and traditional methods’-masi

thanks• Malaysian government reports/statements• Wikipedia.com• Malaysiakini Radio/TV and the Media• Photo Gallery• Gayesian experts like Sharon Bertsch McGrayne