Bayesian Additive Regression Trees, Computational Approaches

Methods based on binary trees play a fundamental role in modern data science. In this article, we give a very focused review of basic Bayesian approaches to tree modeling. Bayesian approaches have some fundamental advantages. Complex models are enhanced with meaningful prior specifications, and Markov chain Monte Carlo provides a framework for useful stochastic search of the model space along with some sense of uncertainty. Bayesian approaches require a specification of a prior in tree space and computation of a high and variable dimension posterior. We provide some computational details that are not readily available in the literature. We also review a few more recent extensions of the basic approaches to illustrate the power and potential of the overall approach.