Semiparametric inference in mixture models with predictive recursion marginal likelihood

• 成果类型: Article
• 署名作者: Martin, Ryan; Tokdar, Surya T.
• 署名单位: Purdue University System; Purdue University; Purdue University in Indianapolis; Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asr030
• 发表日期: 2011
• 页码: 567582
• 关键词: bayesian-analysis; nonparametric problems; distributions; Consistency

摘要

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in the additional unknown structural parameter. As an alternative to existing profile likelihood methods, we treat predictive recursion as a filter approximation by fitting a fully Bayes model, whereby an approximate marginal likelihood of the structural parameter emerges and can be used for inference. We call this the predictive recursion marginal likelihood. Convergence properties of predictive recursion under model misspecification also lead to an attractive construction of this new procedure. We show pointwise convergence of a normalized version of this marginal likelihood function. Simulations compare the performance of this new approach with that of existing profile likelihood methods and with Dirichlet process mixtures in density estimation. Mixed-effects models and an empirical Bayes multiple testing application in time series analysis are also considered.