Spatial Search and Bayes Theorem: A Commentary on Recent Examples from Aircraft Accidents

Abstract

This paper presents a Bayesian search methodology in the context of missing aircraft, as well as a few other related search operations. The search seeks an item hidden in one of n cells. The parameters controlling the search are the prior probabilities (updated during each phase of the search) and the search quality. Assume the search begins in the area with the maximal prior. The expected length of the search depends on how far the item is from that locale (in essence a measure of the quality of the prior), and the search effectiveness parameter. A perfect (error free) search could find the item in a number of steps as a function of the distance of the object from the starting location. Lower quality search can take a lot longer, though it can ultimately be effective. The Bayesian process works by guiding us to the higher likelihood areas based on the results of failed search. It adds value by eliminating unlikely possibilities. The search can have an element of luck in starting its exploration close to the actual item. Real searches, where this was true, were in fact ultimately successful; real searches which were not so fortunate ended in failure.