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Bayes' rule found AF 447

Few realize the key role played by a long-discredited 18th century mathematical theory in finding and recovering the wreckage of AF 447.

After a fruitless two-year search for Air France Flight 447, Bayes’ rule pointed to its most probable location—where it was found after only one week of undersea searching.

The 2009 crash of AF 447 was one of the most mysterious accidents in aviation history. The Airbus took off from Rio de Janeiro on May 31, 2009, bound overnight for Paris. Early in the morning it met an intense high-altitude electrical storm over the South Atlantic and disappeared without a trace with 228 aboard.

Bureau d’Enquêtes et d’Analyses (BEA), the French equivalent of the U.S. Federal Aviation Agency, coordinated the longest, most difficult, most high-tech, and most expensive undersea search ever launched.

To understand why the jet crashed, the BEA needed to find the black boxes housing the cockpit and flight data recordings. But the aviation industry’s standard black box is the size of a shoebox, and they were lost somewhere in an undersea area similar in size and mountainous topography to Switzerland.

After almost two years of fruitless searching, the French agency turned to an American consulting firm to make an exhaustive Bayesian review of the entire search effort.
Bayes’ rule, discovered by English and French mathematicians in the 1700s, has recently swept through the computer world.

Bayes’ rule was used during World War II and the Cold War to find German U-boats; an unarmed H-bomb that fell near Palomares, Spain; the lost nuclear submarine U.S.S. Scorpion; and Soviet submarines during the Cold War. These stories are told in my book, The Theory that Would Not Die: How Bayes’ Rule cracked the Enigma code, hunted down Russian submarines and emerged triumphant from two years of controversy (Yale University Press 2011).

It says that by updating our initial beliefs with objective new information, we can get a new and improved belief. So analysts for Metron Inc. in Reston, Virginia, started their search for AF 447 by incorporating everything that was known before the accident about airplane flight dynamics, area winds and currents, and other aircraft accidents involving loss of control. Metron assigned 70% probability to the credibility of these data. The positions and recovery times of bodies found drifting on the ocean surface were also incorporated into the prior probability but were assigned only a 30% probability because of the turbulent equatorial waters. All this information was organized into consistent scenarios and their uncertainties quantified and weighted.

To update this pre-search information, all available data from the air, surface, and underwater searches were assembled. Finally, Bayes’ rule was used to update the prior pre-search information with the search data.

Introducing the possibility that the pinging alarm signals attached to the black boxes had malfunctioned during the crash pointed to a high-priority area that sonar had not yet explored.

After a one-week undersea search, the wreckage of AF 447 was found on April 3, 2011 under almost 2.5 miles of ocean.

Remarkably, given the fact that even the word Bayes had been too controversial to mention for decades of the 20th century, the French government publicly credited Bayesian methods for pointing to the plane’s most probable resting place.

Soon after finding the wreckage, the BEA returned to the site with a salvage ship and recovered both the flight data recorder and the cockpit voice recorder in working order as well as the remains of 104 victims.

When the BEA issues its final report on the accident scheduled for this summer, remember that the plane was found because of mathematicians working 250 years ago.
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