  We develop a Bayesian "sum-of-trees" model where each tree is constrained by
a regularization prior to be a weak learner, and fitting and inference are
accomplished via an iterative Bayesian backfitting MCMC algorithm that
generates samples from a posterior. Effectively, BART is a nonparametric
Bayesian regression approach which uses dimensionally adaptive random basis
elements. Motivated by ensemble methods in general, and boosting algorithms in
particular, BART is defined by a statistical model: a prior and a likelihood.
This approach enables full posterior inference including point and interval
estimates of the unknown regression function as well as the marginal effects of
potential predictors. By keeping track of predictor inclusion frequencies, BART
can also be used for model-free variable selection. BART's many features are
illustrated with a bake-off against competing methods on 42 different data
sets, with a simulation experiment and on a drug discovery classification
problem.
