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

Bayesian Additive Regression Trees With Parametric Models of Heteroskedasticity