A Note on Bayes Semiparametric Regression

Abstract

In the Bayesian approach to inference, all unknown quantities contained in a probability model for the observed data are treated as random variables. Specifically, the fixed but unknown parameters are viewed as random variables under the Bayesian approach. In this paper, Bayesian approach is employed to making inferences on the semiparametric regression model as mixed model , and we prove some theorems about posterior.

Keywords?Mixed models, Semiparametric regression, Penalized spline, Bayesian inference, Prior density, Posterior density.