Objective Bayes and conditional inference in exponential families

• 成果类型: Article
• 署名作者: Diciccio, Thomas J.; Young, G. Alastair
• 署名单位: Cornell University; Imperial College London
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq002
• 发表日期: 2010
• 页码: 497504
• 关键词: nuisance parameters; gamma-distribution; shape parameter; priors

摘要

Objective Bayes methodology is considered for conditional frequentist inference about a canonical parameter in a multi-parameter exponential family. A condition is derived under which posterior Bayes quantiles match the conditional frequentist coverage to a higher-order approximation in terms of the sample size. This condition is on the model, not on the prior, and it ensures that any first-order probability matching prior in the unconditional sense automatically yields higher-order conditional probability matching. Objective Bayes methods are compared to parametric bootstrap and analytic methods for higher-order conditional frequentist inference.