We investigate the asymptotic behavior of the Bayes factor for regression problems in which observations are not required to be independent and identically distributed and provide general results about consistency of the Bayes factor. Then we specialize our results to the model selection problem in the context of partially linear regression model in which the regression function is assumed to be the additive form of the linear component and the nonparametric component. Specifically, sufficient conditions to ensure Bayes factor consistency are given for choosing between the parametric model and the semiparametric alternative in the partially linear regression model.
