Bayesian semiparametric Regression Using Spline

Abstract

  In this paper, we consider semiparametric regression model where the mean function of this model has two part, the parametric ( first part ) is assumed to be linear function of p-dimensional covariates and nonparametric ( second part ) is assumed to be a smooth penalized spline. By using a convenient connection between penalized splines and mixed models, we can representation semiparametric regression model as mixed model. Bayesian approach is employed to making inferences on the resulting mixed model coefficients, and we prove some theorems about posterior.