  Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to
modeling with ensembles of trees. BART can uncover complex regression functions
with high dimensional regressors in a fairly automatic way and provide Bayesian
quantification of the uncertainty through the posterior. However, BART assumes
IID normal errors. This strong parametric assumption can lead to misleading
inference and uncertainty quantification. In this paper, we use the classic
Dirichlet process mixture (DPM) mechanism to nonparametrically model the error
distribution. A key strength of BART is that default prior settings work
reasonably well in a variety of problems. The challenge in extending BART is to
choose the parameters of the DPM so that the strengths of the standard BART
approach is not lost when the errors are close to normal, but the DPM has the
ability to adapt to non-normal errors.
