Bayes Variable Selection in Semiparametric Linear Models.

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. [ABSTRACT FROM AUTHOR]