In the early morning hours of June 1, 2009, during a flight from Rio de Janeiro to Paris, Air France Flight AF 447 disappeared during stormy weather over a remote part of the Atlantic carrying 228 passengers and crew to their deaths. After two years of unsuccessful search, the authors were asked by the French Bureau d'Enqu\^{e}tes et d'Analyses pour la s\'{e}curit\'{e} de l'aviation to develop a probability distribution for the location of the wreckage that accounted for all information about the crash location as well as for previous search efforts. We used a Bayesian procedure developed for search planning to produce the posterior target location distribution. This distribution was used to guide the search in the third year, and the wreckage was found with one week of undersea search. In this paper we discuss why Bayesian analysis is ideally suited to solving this problem, review previous non-Bayesian efforts, and describe the methodology used to produce the posterior probability distribution for the location of the wreck.Comment: Published in at http://dx.doi.org/10.1214/13-STS420 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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