Dr. Taeryon Choi
Department of Mathematics and Statistics
University of Maryland, Baltimore County

In this talk, we consider a semiparametric regression model where the unknown regression function is the sum of parametric and nonparametric parts. The parametric part is a finite dimensional multiple regression function where as the nonparametric part is represented by an infinite series of orthogonal basis. In this model, we investigate the large sample property of the Bayes factor for testing the parametric null model against the semiparametric alternative model. Under some conditions on the prior and design matrix, we identify the analytic form of the Bayes factor and show that the Bayes factor is consistent, i.e. converges to infinity in probability under the parametric null model, while converges to zero under the semiparametric alternative, as the sample size increases.