A Bayesian approach to additive semiparametric regression

We present a Bayesian approach to estimating an additive semiparametric regression model which is robust to outliers. The unknown curves are estimated by posterior means and are shown to be smoothing splines. By using Markov chain Monte Carlo, an O(Mn) algorithm is produced, where n is the sample size and M is the total number of Markov chain iterations. Previous exact approaches required O(n3) operations making the estimation of large data sets impractical. Efficient methods for estimating the posterior means using mixture and backfitting estimates are developed. The properties of the curve estimates are studied empirically using both simulated and real examples.