A note on Bayes factor consistency in partial linear models

It has become increasingly important to understand the asymptotic behavior of the Bayes factor for model selection in general statistical models. In this paper, we discuss recent results on Bayes factor consistency in semiparametric regression problems where observations are independent but not identically distributed. Specifically, we deal with the model selection problem in the context of partial linear models in which the regression function is assumed to be the additive form of the parametric component and the nonparametric component using Gaussian process priors, and Bayes factor consistency is investigated for choosing between the parametric model and the semiparametric alternative.