View
755
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Further to my earlier upload on this subject, I submit this updated version to keep viewers better informed of my belief in the Bayes Theorem.
Citation preview
the flight mh370 & bayes theoryMasilamani Ramasamy
- a scientific management expert([email protected])
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 NumberChina/Taiwan 154Malaysia 38India 5Indonesia 7Australia 6France 4USA 3New Zealand 2Canada 2Russia 1Italy 1Netherlands 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
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 oceanSite Atlantic Ocean
near 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