Nonparametric regression using Bayesian variable selection

This paper estimates an additive model semiparametrically, while automatically selecting the significant independent variables and the appropriate power transformation of the dependent variable. The nonlinear variables are modeled as regression splines, with significant knots selected from a large number of candidate knots. The estimation is made robust by modeling the errors as a mixture of normals. A Bayesian approach is used to select the significant knots, the power transformation, and to identify outliers using the Gibbs sampler to carry out the computation. Empirical evidence is given that the sampler works well on both simulated and real examples and that in the univariate case it compares favorably with a kernel-weighted local linear smoother. The variable selection algorithm in the paper is substantially faster than previous Bayesian variable selection algorithms.