Air France Flight 447's pathOona Raisanen/Wikimedia Commons
Applying all available information – including wind and water currents, previous flight patterns and underwater drift – Bayes’ Theorem helped French authorities determine where Flight 447 would most likely be. The flight’s black box was then found under more than 12,000 feet of water.
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.
“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.
Stone told Al Jazeera the company is not currently involved in search efforts for Flight MH370, and that at this point it is “highly unlikely” that Bayes’ Theorem is being applied in the search.
But Professor Bradley Efron, statistician at Stanford University, told Al Jazeera that though Bayes’ Theorem is not being applied formally, “the people who are doing the searches are Bayesian.”
“Their search process has a certain Bayesian flavor, but it then got upset when their prior calculations were incorrect.”
Efron was referring to Malaysian authorities coming to a false calculation that the plane had crashed over the Malacca Straits, where they spotted an oil slick thought to have originated from the plane.
Though Bayes’ rule allows for constant modification to a hypothesis, it only works if the situation is similar enough to evidence applied from past incidents.
Searchers' focus on the oil slick in the Malaysia Airlines case would have guided Bayes’ Theorem in the wrong direction because the slick was not related to the missing plane.
A “weakness of Bayes’ theorem is that you have to have reasonably accurate past experiences in order for the theorem to calculate accurately,” Efron said.