  We incorporate heteroskedasticity into Bayesian Additive Regression Trees
(BART) by modeling the log of the error variance parameter as a linear function
of prespecified covariates. Under this scheme, the Gibbs sampling procedure for
the original sum-of- trees model is easily modified, and the parameters for the
variance model are updated via a Metropolis-Hastings step. We demonstrate the
promise of our approach by providing more appropriate posterior predictive
intervals than homoskedastic BART in heteroskedastic settings and demonstrating
the model's resistance to overfitting. Our implementation will be offered in an
upcoming release of the R package bartMachine.
