Bayesian Regression Modeling with Interactions and Smooth Effects

Abstract

There have been many recent suggestions as to how to build and estimate flexible Bayesian regression models, using constructs such as trees, neural networks, and Gaussian processes. Although there is much to commend these methods, their implementation and interpretation can be daunting for practitioners. This article presents a spline-based methodology for flexible Bayesian regression that is quite simple in terms of computation and interpretation. Smooth bivariate interactions are modeled in an economical and apparently novel way, and prior distributions that penalize complexity are used. Predictions can be based on either model selection or model averaging. Taking computation, interpretation, and predictive performance into account, the method is seen to perform well when applied to simulated and real data.

Key Words:

• Bayesian method
• Interaction
• Multiple regression
• Splines