The true detection probability versus the subjective detection probability of a uniformly optimal search plan

TL;DR

This paper explores the differences between true and subjective detection probabilities in uniformly optimal search plans, revealing conditions under which they diverge and their asymptotic behavior.

Contribution

It demonstrates that uniformly optimal search plans may not always be truly optimal and analyzes their true detection probabilities under various priors.

Findings

Uniformly optimal plans can be suboptimal in true detection probability.

True detection probability can be less than that of plans based on different priors.

As search time increases, the true detection probability approaches one.

Abstract

This article investigates the difference between the true detection probability and the subjective probability of a uniformly optimal search plan. Its main contributions are multi-fold. First, it provides a set of examples to show that, in terms of the true detection probability, the uniformly optimal search plan may or may not be optimal. Secondly, it establishes that the true detection probability of the uniformly optimal search plan based on a composite prior can be less than that of the composite uniformly search plan based on different priors. Next, it argues that an open problem is unsolvable. Finally, it shows that the true detection probability of the uniformly optimal search plan converges to one as the search time approaches infinity.