Nonparametric Bayes Conditional Distribution Modeling With Variable Selection

被引:109
|
作者
Chung, Yeonseung [1 ]
Dunson, David B. [2 ]
机构
[1] Harvard Univ, Sch Publ Hlth, Dept Biostat, Boston, MA 02115 USA
[2] Duke Univ, Dept Stat Sci, Durham, NC 27707 USA
关键词
Conditional distribution estimation; Hypothesis testing; Kernel stick-breaking process; Mixture of experts; Stochastic search variable selection; PROCESS MIXTURE-MODELS; HIERARCHICAL MIXTURES; REGRESSION-MODELS; OF-EXPERTS; INFERENCE; PRIORS; LIKELIHOOD; DENSITIES; LASSO;
D O I
10.1198/jasa.2009.tm08302
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
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.
引用
收藏
页码:1646 / 1660
页数:15
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