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Math equation could help find missing Malaysian pl
Days after a Malaysian airliner with 239 people aboard went missing en route to Beijing, searchers are still struggling to find any confirmed sign of the plane. Authorities have acknowledged that they didn't even know what direction it was heading when it disappeared.
In 2009, Air France Flight 447 en route to Paris from Rio de Janeiro vanished over the Atlantic Ocean, triggering the most expensive and exhaustive search effort ever conducted for a plane. After two years, officials could only narrow the location of the plane's black box down to an area the size of Switzerland.
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.
"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, author of "The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy."
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.
Bayes' Theorem, which is also used in Google's driverless cars and predictions in stock markets, is based on probability. Because the theorem starts with a hypothesis — something McGrayne said "can be very subjective" — it had been seen as controversial until the 1960s. But because it forces researchers to change their hypothesis with each new piece of information, the probability becomes more accurate.
The theorem was used in World War II to locate German U-boats and the lost nuclear submarine U.S.S. Scorpion. It was also used during the Cold War to spot Soviet submarines.
"The AF 447 search is rooted in Bayesian inference," Lawrence D. Stone, chief scientist at Virginia-based scientific consultancy Metron — which was contacted to apply Bayes' Theorem in the search for the Air France plane — wrote in ORMS Today magazine in 2011. Bayes' Theorem "allows the organization of available data with associated uncertainties and computation of the PDF (probability distribution function) for target location given these data," he said.
Despite assistance from Australia, China, Thailand, Indonesia, Singapore, Vietnam, Philippines and the United States, Malaysian search efforts are even further from locating Flight MH370. The search area has been expanded to almost 27,000 square nautical miles — an area roughly equivalent to the state of Indiana — authorities said. That's more than 10,000 nautical square miles larger than the search for Air France Flight 447, before Bayes' Theorem was applied.
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.
