## The Annals of Statistics

### Optimal Sequential Search: A Bayesian Approach

#### Abstract

To the classical model of searching for one object out of $n$, we add uncertainty about the parameters $\mathbf{\pi}$ of the distribution of the $n$ objects among the $m$ boxes. Adopting a Bayesian approach, we study the optimal sequential search strategy. For the case $n = 1$, we obtain a generalization of the fundamental result of Blackwell: the strategy which searches at each stage in the "most inviting" box is optimal. This strategy is also optimal for $m = 2$ and arbitrary $n$. However, for $n > 1$ the optimal strategy may be very different from that of the classical model, even when the uncertainty about $\mathbf{\pi}$ is very small.

#### Article information

Source
Ann. Statist. Volume 13, Number 3 (1985), 1213-1221.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349665

Digital Object Identifier
doi:10.1214/aos/1176349665

Mathematical Reviews number (MathSciNet)
MR803767

Zentralblatt MATH identifier
0589.90045

JSTOR