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 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.
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