Information Theory and the Optimal Detection Search

This paper establishes a connection between information theory and search theory. In the case of an exponential detection function we show that the search that maximizes the probability of detection also minimizes the information content of the posterior distribution. We also show that if the search plan that maximizes the probability of detection also minimizes the information content of the posterior distribution, then the detection function is exponential. We prove our results in both the continuous and discrete cases.