Bayesian Nonparametric Modelling with the Dirichlet Process Regression Smoother

In this paper we discuss implementing Bayesian fully nonparametric regression by defining a process prior on distributions which depend on covariates. We consider the problem of centring our process over a class of regression models and propose fully nonparametric regression models with flexible location structures. We also introduce a non-trivial extension of a dependent finite mixture model proposed by Chung and Dunson (2007) to a dependent infinite mixture model and propose a specific prior, the Dirichlet Process Regression Smoother, which allows us to control the smoothness of the process. Computational methods are developed for the models described. Results are presented for simulated and actual data examples.