A Bayesian χ2 test for goodness-of-fit

• 成果类型: Article
• 署名作者: Johnson, VE
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000616
• 发表日期: 2004
• 页码: 2361-2384
• 关键词: composite null models; square test; hierarchical-models; P-values; number; selection; checking

摘要

This article describes an extension of classical chi(2) goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involves evaluating Pearson's goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptotically distributed as a chi(2) random variable on K - 1 degrees of freedom, independently of the dimension of the underlying parameter vector. By examining the posterior distribution of this statistic, global goodness-of-fit diagnostics are obtained. Advantages of these diagnostics include ease of interpretation, computational convenience and favorable power properties. The proposed diagnostics can be used to assess the adequacy of a broad class of Bayesian models, essentially requiring only a finite-dimensional parameter vector and conditionally independent observations.