Bayesian goodness-of-fit testing using infinite-dimensional exponential families

• 成果类型: Article
• 署名作者: Verdinelli, I; Wasserman, L
• 署名单位: Sapienza University Rome; Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1215-1241
• 关键词: nonparametric density-estimation; posterior distributions; orthogonal series; MODEL; inference

摘要

dWe develop a nonparametric Bayes factor for testing the fit of a parametric model. We begin with a nominal parametric family which we then embed into an infinite-dimensional exponential family. The new model then has a parametric and nonparametric component. We give the log density of the nonparametric component a Gaussian process prior. An asymptotic consistency requirement puts a restriction on the form of the prior, leaving us with a single hyperparameter for which we suggest a default value based on simulation experience. Then we construct a Bayes factor to test the nominal model versus the semiparametric alternative. Finally, we show that the Bayes factor is consistent. The proof of the consistency is based on approximating the model by a sequence of exponential families.