Bayesian regression modeling with interactions and smooth effects

There have been many recent suggestions as to how to build and estimate fle xible Bayesian regression models, using constructs such as trees, neural ne tworks, and Gaussian processes. Although there is much to commend these met hods, their implementation and interpretation can be daunting for practitio ners. This article presents a spline-based methodology for flexible Bayesia n regression that is quite simple in terms of computation and interpretatio n. Smooth bivariate interactions are modeled in an economical and apparentl y novel way, and prior distributions that penalize complexity are used. Pre dictions can be based on either model selection or model averaging. Taking computation, interpretation, and predictive performance into account, the m ethod is seen to perform well when applied to simulated and real data.