BAYESIAN NONPARAMETRIC MCMC FOR LARGE VARIABLE SELECTION PROBLEMS

J. Sunil Rao

Case Western Reserve University

(Joint work with Hemant Ishwaran, Cleveland Clinic)

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Embedding the linear regression problem in the form of a Bayesian nonparametric hierarchical model subject to a truncated Dirichlet process is an effective approach for selecting variables in problems with large dimensions and high correlation. In this stochastic approach, model selection is based on posterior rank and score values for each regression parameter, with variable selection intimately tied to correlation structure. Overall, we find that our nonparametric procedure generally outperforms its limiting parametric analogue in low/moderate correlation settings. With medium to high correlation both procedures do equally well through the use of a shrinkage estimator. Both the nonparametric and parametric procedures include a complexity parameter for controlling model size that are automatically fitted as part of the Gibbs procedure.

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