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Abstract:
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In the Bayesian paradigm model selection can logically be done either through the specification of the prior or through specification of the utility. Logically, it would seem that in most applications, the true underlying goal of the study would motivate an approach largely based on utility. However, while there are notable exceptions, the majority of the literature considers model selection via the prior. In "BART: Bayesian Additive Regression Trees," Chipman, George, and McCulloch introduced an easy to use Bayesian approach to finding the function f in the basic model y = f(x) + error, where x may be high dimensional (see the R-package BayesTree). CGM briefly discuss variable selection through the prior. In this work we consider several approaches to model selection and contrast their effectiveness on a variety of applications.
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