Bayes Variable Selection in Semiparametric Linear Models

Suprateek Kundu and David B. Dunson

Journal of the American Statistical Association, 2014, vol. 109, issue 505, 437-447

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 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.

Date: 2014
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DOI: 10.1080/01621459.2014.881153

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