Fuzzy sets in semiparametric Bayes Regression

Abstract

In this paper, we consider semi parametric 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 semi parametric regression model as mixed model. Bayesian approach to semi parametric regression is described using fuzzy sets and membership functions. The membership functions are interpretedas likelihood functions for the model. Bayesian approach is employed to making inferences on the resulting mixed model coefficients, and we prove some theorems about posterior and Bayes factor.