LINDA WERTHEIMER, HOST:
The search for survivors on the missing Malaysian Airlines flight took a dark turn yesterday when Malaysia's prime minister said his government now believes the plane went down somewhere in the Indian Ocean and that all 239 people aboard are dead.
DAVID GREENE, HOST:
They based that on a new assessment of signals sent from the aircraft to a satellite, but they can't tell exactly where the aircraft might have gone down.
WERTHEIMER: Back in 2009, when an Air France flight was lost over the Atlantic, it took a statisticians' hunch and a mathematical theorem to pinpoint the wreckage.
NPR's Geoff Brumfiel reports on how the study of probabilities can help in an ocean search.
GEOFF BRUMFIEL, BYLINE: After Malaysian Air Flight 370 disappeared from radars, it continued to leave a little trail of clues. Every hour the aircraft's antenna pinged a satellite high above the Earth. The pings didn't contain location data, but the company that owns the satellite, Inmarsat, was able to tell something about the plane's whereabouts.
Yesterday, a new analysis narrowed the search to the Southern Indian Ocean. The trail of pings ends there.
CHRIS MCLAUGHLIN: We have really exhausted what a single ping once an hour can do.
BRUMFIEL: Chris McLaughlin is a senior vice president with Inmarsat. He says the satellite data has yielded every clue it can.
MCLAUGHLIN: The reality is that we can't say for definite where it came down. We can't say for definite what the final point was.
BRUMFIEL: Without a final point, it's hard to know where to look. There are thousands and thousands of square miles that need to be combed and this is where statistics might help. Colleen Keller is a senior analyst with Metron Corporation. Metron's in a very particular business, using mathematics to look for things that are lost underwater. Keller first worked on air crashes in 2009 after Air France Flight 449 disappeared over the Atlantic Ocean. [POST-BROADCAST CORRECTION: It was Air France Flight 447 that disappeared, not 449.]
COLLEEN KELLER: I arrived there a month and a half after the crash.
BRUMFIEL: Search teams had started by listening for underwater signals from the airplane's two black boxes, but no one ever heard anything.
KELLER: They had finished the underwater beacon search, came up unsuccessful, were kind of throwing up their hands, okay, what do we do next, we're in for a protracted underwater search at this point.
BRUMFIEL: Keller began weighing the probabilities of certain events. What was the chance of mechanical failure or pilot error or what were the odds that floating debris on the surface was near the submerged wreckage? She combined all sorts of different information into a single mathematical framework.
KELLER: It's an actual mathematical theorem called Bayes Theory.
BRUMFIEL: A theory proposed by Thomas Bayes in the 18th century.
KELLER: Which allows you to keep everything on the table and combine things into an overall picture of what you know.
BRUMFIEL: In a complicated scenario like an accident, intuition isn't good enough. Arnold Barnett is a statistician at MIT. He says Bayes Theorem helps.
ARNOLD BARNETT: A certain piece of information is often much more telling than you might intuitively think. Or it might be much less informative than you intuitively think. Bayes Theorem is calm. You know, it doesn't have emotions and it may actually tell us things we would not have realized otherwise.
BRUMFIEL: Bayes Theorem is especially good for searching because it allows you to update all the odds after you've looked in a certain place. But, Barnett adds, Bayes Theorem can only provide an estimate, a guess.
BARNETT: Bayes Theorem can't find the plane, period. It can, at best, change the odds.
BRUMFIEL: Colleen Keller, the analyst who searched for that Air France flight, knows that it's hard to get all the odds just right. In her initial guess of where to look, Keller eliminated huge swaths of ocean floor because nobody heard a signal from the plane's black boxes. But it turned out, against the odds, both of the black boxes were damaged.
Two years later, Keller did some recalculations based on that unlikely possibility and then they found the wreckage in under a week. For Keller, the lesson is clear.
KELLER: Sometimes the probabilities will turn around and bite you.
BRUMFIEL: An educated guess can help the search for Malaysian Air Flight 370, but finding it is still going to take luck. Geoff Brumfiel, NPR News. Transcript provided by NPR, Copyright NPR.