## Bayes’ Theorem and the The Search for Missing Planes

In 2009, when Air France Flight 447 disappeared over the Atlantic Ocean, mathematician Colleen Keller on Metron went to work using Bayes’ Theorem to develop a probabilistic framework that was aimed at identifying where the fallen plane might potentially be.

The beauty of Bayes’ theorem is that “it is 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”, according to Sharon McGrayne, author of “Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy”. With so much ambiguity in the search for plane crashes, the Bayes’ Theorem “allows the organization of available data with associated uncertainties”, says Lawrence Stone, Chief Scientist at Metron. This hypothesis can be changed and improved when more and more information is gathered.

In the case of the search for Air France Flight 447, the first application of the developed Bayesian model turned up nothing, but after more information raised, Keller and her colleagues at Metron were able to revise and improve their model, and this time were able to pinpoint the search field. Armed with the new model, searchers were able to find the crash site within four or five days. The weakness with Bayes’ Theorem is that its accuracy depends on the accuracy of past data, and information. Thus, with the more unpredictable Indian Ocean, Bayes’ Theorem may not work as accurately but may still help with narrowing down the search site for the more recently missing Malaysian Airlines flight.

References:

http://america.aljazeera.com/articles/2014/3/12/mathematical-equationcouldhelpfindmissingmalaysianplane.html

http://www.npr.org/sections/thetwo-way/2014/03/25/294390476/can-a-250-year-old-mathematical-theorem-find-a-missing-plane