Nonparametric Bayes Conditional Distribution Modeling With Variable Selection

• 成果类型: Article
• 署名作者: Chung, Yeonseung; Dunson, David B.
• 署名单位: Harvard University; Harvard T.H. Chan School of Public Health; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2009.tm08302
• 发表日期: 2009
• 页码: 1646-1660
• 关键词: process mixture-models; hierarchical mixtures; regression-models; of-experts; inference; priors; likelihood; densities; Lasso

摘要

This article considers a methodology for flexibly characterizing the relationship between a response and multiple predictors. Goals are (1) to estimate the conditional response distribution addressing the distributional changes across the predictor space, and (2) to identify important predictors for the response distribution change both within local regions and globally. We first introduce the probit stick-breaking process (PSBP) as a prior for an uncountable collection of predictor-dependent random distributions and propose a PSBP mixture (PSBPM) of normal regressions for modeling the conditional distributions. A global variable selection structure is incorporated to discard unimportant predictors, while allowing estimation of posterior inclusion probabilities. Local variable selection is conducted relying on the conditional distribution estimates at different predictor points. An efficient stochastic search sampling algorithm is proposed for posterior computation. The methods are illustrated through simulation and applied to an epidemiologic study.