An Alternate Parameterization for Bayesian Nonparametric/Semiparametric Regression

We present a new procedure for nonparametric Bayesian estimation of regression functions. Specifically, our method makes use of an idea described in Frühwirth-Schnatter and Wagner (2010) to impose linearity exactly (conditional upon an unobserved binary indicator), yet also permits departures from linearity while imposing smoothness of the regression curves. An advantage of this approach is that the posterior probability of linearity is essentially produced as a by-product of the procedure. We apply our methods in both generated data experiments as well as in an illustrative application involving the impact of body mass index (BMI) on labor market earnings.