Bayesian search theory is the application of Bayesian statistics to the search for lost objects. It has been used several times to find lost sea vessels, for example USS Scorpion, and has played a key role in the recovery of the flight recorders in the Air France Flight 447 disaster of 2009. It has also been used in the attempts to locate the remains of Malaysia Airlines Flight 370. Procedure The usual procedure is as follows: Formulate as many reasonable hypotheses as possible about what may have happened to the object. For each hypothesis, construct a probability density function for the location of the object. Construct a function giving the probability of actually finding an object in location X when searching there if it really is in location X. In an ocean search, this is usually a function of water depth — in shallow water chances of finding an object are good if the search is in the right place. In deep water chances are reduced. Combine the above information coherently to produce an overall probability density map. (Usually this simply means multiplying the two functions together.) This gives the probability of finding the object by looking in location X, for all possible locations X. (This can be visualized as a contour map of probability.) Construct a search path which starts at the point of highest probability and 'scans' over high probability areas, then intermediate probabilities, and finally low probability areas. Revise all the probabilities continuously during the search. For example, if the hypotheses for location X imply the likely disintegration of the object and the search at location X has yielded no fragments, then the probability that the object is somewhere around there is greatly reduced (though not usually to zero) while the probabilities of its being at other locations is correspondingly increased. The revision process is done by applying Bayes' theorem. In other words, first search where it most probably will be found, then search where finding it is less probable, then search where the probability is even less (but still possible due to limitations on fuel, range, water currents, etc.), until insufficient hope of locating the object at acceptable cost remains. The advantages of the Bayesian method are that all information available is used coherently (i.e., in a "leak-proof" manner) and the method automatically produces estimates of the cost for a given success probability. That is, even