title: Bayes variable selection in semiparametric linear models.
abstract: There is a rich literature on Bayesian variable selection for parametric models. Our focus is on generalizing methods and asymptotic theory established for mixtures ofg-priors to semiparametric linear regression models having unknown residual densities. Using a Dirichlet process location mixture for the residual density, we propose a semiparametricg-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 ongeven when the number of candidate predictorspis allowed to increase much faster than sample sizen, while making sparsity assumptions on the true model size.
authors: Postdoctoral Research Associate in the Dept. of Statistics, Texas A&M University, College Station, TX 77843, USA.
authors: Suprateek
authors: S
authors: Kundu
authors: Arts & Sciences Distinguished Professor in Dept. Statistical Science, Duke University, Durham, NC 27708, USA.
authors: David B
authors: DB
authors: Dunson
keywords: Asymptotic theory; Bayes factor; Large p; Model selection; Posterior consistency; Stochastic search variable selection; Subset selection; g-prior; small n