P values for composite null models

• 成果类型: Article
• 署名作者: Bayarri, MJ; Berger, JO
• 署名单位: University of Valencia; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2669749
• 发表日期: 2000
• 页码: 1127-1142
• 关键词: inference; frequentist; hypothesis

摘要

The problem of investigating compatibility of an assumed model with the data is investigated in the situation when the assumed model has unknown parameters. The most frequently used measures of compatibility are p values, based on statistics T for which large values are deemed to indicate incompatibility of the data and the model. When the null model has unknown parameters. ?, values are not uniquely defined. The proposals for computing a p value in such a situation include the plug-in and similar p values on the frequentist side, and the predictive and posterior predictive p values on the Bayesian side. We propose two alternatives, the conditional predictive p value and the partial posterior predictive p value, and indicate their advantages from both Bayesian and frequentist perspectives.