Model selection in spline nonparametric regression

A Bayesian approach is presented for model selection in nonparametric regression with Gaussian errors and in binary nonparametric regression. A smoothness prior is assumed for each component of the model and the posterior probabilities of the candidate models are approximated using the Bayesian information criterion. We study the model selection method by simulation and show that it has excellent frequentist properties and gives improved estimates of the regression surface. All the computations are carried out efficiently using the Gibbs sampler.