THE ROLE OF THE NEYMAN-PEARSON LEMMA IN THE THEORY OF DISCRETE SEARCH
YALE UNIV NEW HAVEN CT COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
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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 subj,k that the object is found in the j th search of the k th box are disjoint, and P sub jk PrE 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.
- Economics and Cost Analysis