Malaysia

An 18th century maths equation may hold answer to finding missing plane, say scientists

A military officer works on a map onboard a Royal Malaysian Air Force CN235 aircraft during a Search and Rescue (SAR) operation to find the missing Malaysia Airlines flight MH370, in the Straits of Malacca today. – Reuters pic, March 13, 2014.A military officer works on a map onboard a Royal Malaysian Air Force CN235 aircraft during a Search and Rescue (SAR) operation to find the missing Malaysia Airlines flight MH370, in the Straits of Malacca today. – Reuters pic, March 13, 2014.Scientists believe the solution to finding Malaysia Airlines flight MH370 may lie with a mathematical equation.

Speaking to Al Jazeera, they say that Bayes' Theorem, an 18th century mathematical equation, could help to locate the missing plane which dozens of authorities worldwide have not been able to after five days of search and rescue operations.

“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,” said Sharon Bertsch McGrayne, who has authored a book explaining the method in layman's language, The Theory That Would Not Die.

And the hypothesis is subject to change, based on probability, but can still be used with the theorem. Pretty much based on the concept of learning from experience, one can say.

It is because of this character of the formula - forcing researchers to change their hypothesis with each new information - that the probability becomes more accurate.

According Lawrence D. Stone, chief scientist at Virginia-based consultancy Metron whose help was sought to apply Bayes’ Theorem in the Air France incident, Bayes’ Theorem “allows the organisation of available data with associated uncertainties and computation of the PDF (probability distribution function) for target location given these data".

In the past, Bayes’ Theorem, said to be discovered by an amateur mathematician in the 1740s and modernised by French scientist Pierre Simon Laplace, had 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.

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.

Stone told Al Jazeera that in the current search for flight MH370, it is “highly unlikely” that Bayes’ Theorem is being applied.

That is not to suggest it is totally absent.

Bayes' Theorem is pervasive, and those involved in the current search have applied a certain Bayesian flavour in their search, "but it then got upset when their prior calculations were incorrect,” said statistician Professor Bradley Efron of Stanford University, as quoted by Al Jazeera, referring to the conclusion by Malaysian authorities that the MAS plane could have ended up in the Strait of Malacca.

Bayes' Theorem, after all, is all about learning from experience, which is probably why Efron said one would need "reasonably accurate past experiences" for the theorem to work. In other words, to calculate accurately to locate the plane. – March 13, 2014.

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