Nonparametric Bayes conditional distribution modeling with variable selection

Yeonseung Chung and David B. Dunson

Department of Biostatistics, University of North Carolina at Chapel Hill and Department of Statistical Science, Duke University

May 2008

This article considers 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 with local regions and globally. We first introduce the probit stick-breaking process (PSBP) as a prior for an uncountable collection of predictor-dependent random probability measures, 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 algorithm is proposed for posterior computation. The methods are illustrated through simulation and applied to an epidemiologic study.

Keywords: Conditional distribution estimation; Kernel stick-breaking process; Mixture of experts; Hypothesis testing; Stochastic search variable selection.

The manuscript is available in PDF formats.