Bayesian coverage optimization models

Finding a subset collection that provides optimal population coverage is a frequently encountered deterministic problem. A random sample is often used to formulate the optimal coverage (OC) model, which is then used to select the subsets that provide the estimated optimal population coverage. Such problems are ubiquitous and occur in both the public and private sectors; examples include media selection, placement of municipal services such as sirens and waste dumps, and reserve site selection. Conceptualizing sample elements as counts in a contingency table, we show how decision-makers can combine prior information with sample data to help formulate OC models. We consider conjugate and vague priors with classical and empirical Bayesian interpretations. We show that the predictive approach yields a common marketing exposure model that has previously been justified empirically. Finally, we demonstrate the potential importance of our results on problems generated from a well-known example from the literature.