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.
Citation
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