Case Studies in Bayesian Statistical Modelling and Analysis

19

Bayesian Classification and Regression Trees

Rebecca A. O’Leary¹, Samantha Low Choy^2,4, Wenbiao Hu³ and Kerrie L. Mengersen²

¹Department of Agriculture and Food, Western Australia, Australia

²Queensland University of Technology, Brisbane, Australia

³University of Queensland, Brisbane, Australia

⁴Cooperative Research Centre for National Plant Biosecurity, Australia

19.1 Introduction

Classification and regression trees (CARTs) are binary decision trees, which are built by repeatedly splitting the predictor space according to splitting rules of the predictor variables in order to best classify or estimate a response variable (Breiman et al. 1984). These binary decision rules may be easily interpreted as a sequence of if–then–else statements. Each if-clause selects cases according to whether they fall below or above a threshold on a single predictor. The then-clause estimates the average response in these cases. This modelling approach facilitates the identification and description of complex nonlinear interactions between predictor variables, such as combinations of habitat variables describing an ecological niche, or gene–gene interactions that explain a disease. In contrast, with linear regression analysis (Chapter 4) usually only linear and low-order polynomial effects are examined, and it is often difficult to determine nonlinear interactions.

CARTs are popular because they are easy to interpret due to their binary nature and simplistic graphical output. Moreover, they have ...