  We introduce Bayesian additive regression trees (BART) for log-linear models
including multinomial logistic regression and count regression with
zero-inflation and overdispersion. BART has been applied to nonparametric mean
regression and binary classification problems in a range of settings. However,
existing applications of BART have been limited to models for Gaussian "data",
either observed or latent. This is primarily because efficient MCMC algorithms
are available for Gaussian likelihoods. But while many useful models are
naturally cast in terms of latent Gaussian variables, many others are not --
including models considered in this paper.
  We develop new data augmentation strategies and carefully specified prior
distributions for these new models. Like the original BART prior, the new prior
distributions are carefully constructed and calibrated to be flexible while
guarding against overfitting. Together the new priors and data augmentation
schemes allow us to implement an efficient MCMC sampler outside the context of
Gaussian models. The utility of these new methods is illustrated with examples
and an application to a previously published dataset.
