  Bayesian additive regression trees have seen increased interest in recent
years due to their ability to combine machine learning techniques with
principled uncertainty quantification. The Bayesian backfitting algorithm used
to fit BART models, however, limits their application to a small class of
models for which conditional conjugacy exists. In this article, we greatly
expand the domain of applicability of BART to arbitrary \emph{generalized BART}
models by introducing a very simple, tuning-parameter-free, reversible jump
Markov chain Monte Carlo algorithm. Our algorithm requires only that the user
be able to compute the likelihood and (optionally) its gradient and Fisher
information. The potential applications are very broad; we consider examples in
survival analysis, structured heteroskedastic regression, and gamma shape
regression.
