Posterior propriety and admissibility of hyperpriors in normal hierarchical models

• 成果类型: Article
• 署名作者: Berger, JO; Strawderman, W; Tang, DJ
• 署名单位: Duke University; Novartis; Novartis USA; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000075
• 发表日期: 2005
• 页码: 606-646
• 关键词: Covariance matrices; minimax estimators; bayes estimator; EMPIRICAL BAYES; priors

摘要

Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably inferior performance. As an extreme, but not uncommon, example use of the wrong hyperparameter priors can even lead to impropriety of the posterior. For exchangeable hierarchical multivariate normal models, we first determine when a standard class of hierarchical priors results in proper or improper posteriors. We next determine which elements of this class lead to admissible estimators of the mean under quadratic loss; such considerations provide one useful guideline for choice among hierarchical priors. Finally, computational issues with the resulting posterior distributions are addressed.