Objective Priors for Discrete Parameter Spaces

• 成果类型: Article
• 署名作者: Berger, James O.; Bernardo, Jose M.; Sun, Dongchu
• 署名单位: Duke University; University of Valencia; East China Normal University; University of Missouri System; University of Missouri Columbia
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.682538
• 发表日期: 2012
• 页码: 636-648
• 关键词: bayesian-estimation; distributions; inference; size

摘要

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.