Bayesian treed response surface models

Tree-based regression and classification, popularized in the 1980s with the advent of the classification and regression trees (CART) has seen a recent resurgence in popularity alongside a boom in modern computing power. The new methodologies take advantage of simulation-based inference, and ensemble methods, to produce higher fidelity response surfaces with competitive out-of-sample predictive performance while retaining many of the attractive features of classic trees: thrifty divide-and-conquer nonparametric inference, variable selection and sensitivity analysis, and nonstationary modeling features. In this paper, we review recent advances in Bayesian modeling for trees, from simple Bayesian CART models, treed Gaussian process, sequential inference via dynamic trees, to ensemble modeling via Bayesian additive regression trees (BART). We outline open source R packages supporting these methods and illustrate their use.