Bayes Variable Selection in Semiparametric Linear Models

• 成果类型: Article
• 署名作者: Kundu, Suprateek; Dunson, David B.
• 署名单位: Texas A&M University System; Texas A&M University College Station; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.881153
• 发表日期: 2014
• 页码: 437-447
• 关键词: diabetes-mellitus; Consistency; shrinkage; mixtures

摘要

There is a rich literature on Bayesian variable selection for parametric models. Our focus is on generalizing methods and asymptotic theory established for mixtures of g-priors to semiparametric linear regression models having unknown residual densities. Using a Dirichlet process location mixture for the residual density, we propose a semiparametric g-prior which incorporates an unknown matrix of cluster allocation indicators. For this class of priors, posterior computation can proceed via a straightforward stochastic search variable selection algorithm. In addition, Bayes' factor and variable selection consistency is shown to result under a class of proper priors on g even when the number of candidate predictors p is allowed to increase much faster than sample size n, while making sparsity assumptions on the true model size.