The document discusses the application of Bayes' Theorem in understanding the mystery surrounding the disappearance of Malaysia Airlines Flight MH370. It outlines the mathematical and statistical underpinnings of Bayes' Theorem, emphasizes the importance of updating beliefs with new information, and provides examples of its successful applications in historical incidents. Ultimately, it suggests that using scientific principles, rather than emotional reasoning, may lead to locating the missing plane.

1. Flight MH370
& The Bayes Theory
By
Masilamani Ramasamy
Leadership & Scientific Management
Consultant
(misilamani@yahoo.com)

2. MH370

3. 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

4. probability theory
rooted in,
• the science of
Statistics
• the science of
Mathematics
• the probability of an
event occurring
• the analysis of
random phenomena

5. 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 154
Malaysia 38
India 5
Indonesia 7
Australia 6
France 4
USA 3
New Zealand 2
Ukraine 2
Canada 2
Russia 1
Italy 1
Netherlands 1
Austria 1

6. 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 Lines
Aircraft Age: 11years 10
months
Aircraft Type: Boeing 777 ER
Flight No: MH370(shared with
China Southern Airlines)
Passengers travelled: 227
Crew Travelled: 12
Nationalities: 14
Take Off Time: 12.41 am
From: Kuala Lumpur, Malaysia
To: Beijing, China

7. 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

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

9. 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

10. 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

11. 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"

12. 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

13. 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

14. EVENT or
OCCURENCE
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 & awards
numbers drawn or winning
patterns 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

15. 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

16. 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

17. how
because of,
• this character of the formula
• forcing researchers to change
their hypothesis with each new
information
• that the probability becomes
more accurate

18. 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".

19. 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

20. 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…..

21. 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

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

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