We consider semiparametric regression model where the mean function of this model has two parts, the parametric is assumed to be linear function of p-dimensional covariates and nonparametric is assumed to be a smooth penalized spline. By using a convenient connection between penalized splines and mixed models, we can represent semiparametric regression model as a mixed model. Bayesian approach is employed to make inferences on the resulting mixed model coefficients, and we prove some theorems about posterior. We also investigate the large sample property of the Bayes factor for testing the...

We considered the linear one- way repeated measurements model which has only one within units factor and one between units factor incorporating univariate random effects as well as the experimental error term. A Bayesian approach based on Markov Chain Monte Carlo (MCMC) is employed to mak inferences on the one- way repeated measurements model. Furthermore, the Bayesian approach to the one-way repeated measurement model is described after representing the model as a mixed model. We investigated the asymptotic properties of the Bayes factor for testing the fixed effects linear one- way repeated...