Bayes Variable Selection in Semiparametric Linear Models

• Published in: Journal of the American Statistical Association Vol. 109; no. 505; pp. 437 - 447
• Main Authors: Kundu, Suprateek, Dunson, David B.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 01.03.2014; Taylor & Francis Group, LLC; Taylor & Francis Ltd
• Subjects: algorithms; Asymptotic methods; Asymptotic properties; Asymptotic theory; Bayes' factor; Bayesian analysis; Candidates; Diabetes; Feature selection; g-prior; Large p, small n; Linear analysis; Linear models; Linear regression; Marginalization; Matrix; Mixtures; Model selection; Obesity; Parametric models; Posterior consistency; Regression analysis; Sample size; Simulation; Statistics; Stochastic models; Stochastic search variable selection; Subset selection; Theory and Methods; Type 2 diabetes mellitus; Stochastic search variable selection; small n; Model selection; Posterior consistency; Bayes factor; Asymptotic theory; Large p; Subset selection; g-prior
• ISSN: 1537-274X; 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2014.881153

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.