Objective priors for the bivariate normal model

• 成果类型: Article
• 署名作者: Berger, James O.; Sun, Dongchu
• 署名单位: Duke University; University of Missouri System; University of Missouri Columbia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS501
• 发表日期: 2008
• 页码: 963-982
• 关键词: posterior distributions; bayesian-inference; probability

摘要

Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of inference (e.g., Bayesian, frequentist, fiducial) and the criteria involved in deciding on optimal objective priors (e.g., ease of computation, frequentist performance, marginalization paradoxes). Summary recommendations as to optimal objective priors are made for a variety of inferences involving the bivariate normal distribution. In the course of the investigation, a variety of surprising results were found, including the availability of objective priors that yield exact frequentist inferences for many functions of the bivariate normal parameters, including the correlation coefficient.