THE ROLE OF THE NEYMAN-PEARSON LEMMA IN THE THEORY OF DISCRETE SEARCH
Joseph Born Kadane · 1967
Abstract : Suppose an object is hidden in one of n boxes. It is in box k with probability p sub k, k = 1, ..., n. If it is in the k th box, a search of the k th box may overlook it with probability alpha sub k, 0 alpha sub k 1. The events E sub(j,k) that the object is found in the j th search of the k th box are disjoint, and P sub jk = Pr(E sub j,k) = p sub k alpha sub k to the (j-1) power (1-alpha sub k) for k = 1, ..., n and all positive integers j. Suppose also that each search of box k costs c sub k 0. The main problem considered in this paper is how to search in order to maximize the probability of finding the object spending no more than a fixed amount C.