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January, 1977 Strongly Optimal Policies in Sequential Search with Random Overlook Probabilities
Gaineford J. Hall Jr.
Ann. Statist. 5(1): 124-135 (January, 1977). DOI: 10.1214/aos/1176343745

Abstract

Assume a searcher is hunting for an object which has been hidden in one of $N$ regions or cells, with initial prior probability $p_i^1$ that it is in cell $i$. Suppose that to each $i$ there corresponds a sequence $\{\alpha_{ij}\}_{j \geqq 1}$ of random variables, where $\alpha_{ij}$ describes the chances that the searcher will fail to find the object on the $j$th search of $i$, given that the object is in $i$. The joint distribution of $\{\alpha_{ij}: 1 \leqq i \leqq N, j \geqq 1\}$ is known to the searcher. Under a certain monotonicity condition on the $\alpha_{ij}$'s, it is shown that to maximize the probability of finding the object in at most $n_0$ stages of search, the one-stage look ahead rule is optimal. In an earlier paper concerning a related problem, Hall assumed $\{\alpha_{1j}\}_{j \geqq 1}, \cdots, \{\alpha_{N j}\}_{j \geqq 1}$ were independent processes, whereas we allow them to be dependent. Our result is new for independent processes as well.

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Gaineford J. Hall Jr.. "Strongly Optimal Policies in Sequential Search with Random Overlook Probabilities." Ann. Statist. 5 (1) 124 - 135, January, 1977. https://doi.org/10.1214/aos/1176343745

Information

Published: January, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0363.90061
MathSciNet: MR434485
Digital Object Identifier: 10.1214/aos/1176343745

Subjects:
Primary: 90B40
Secondary: 62L05 , 90C40

Keywords: mixture of Dirichlet processes , random overlook probability , sequential search , Strongly optimal policy

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 1 • January, 1977
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