Objective Priors for Discrete Parameter Spaces

This article considers the development of objective prior distributions for discrete parameter spaces. Formal approaches to such development—such as the reference prior approach—often result in a constant prior for a discrete parameter, which is questionable for problems that exhibit certain types of structure. To take advantage of structure, this article proposes embedding the original problem in a continuous problem that preserves the structure, and then using standard reference prior theory to determine the appropriate objective prior. Four different possibilities for this embedding are explored, and applied to a population-size model, the hypergeometric distribution, the multivariate hypergeometric distribution, the binomial-beta distribution, and the binomial distribution. The recommended objective priors for the first, third, and fourth problems are new.