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Bayesian Additive Regression Trees With Parametric Models of Heteroskedasticity
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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 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.
Forward citations
Cited by 2 Pith papers
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A negative binomial soft BART model summarized with ALE is applied to Atlanta asthma ED data, yielding a harmful ozone association, a negative NO2 association, and temperature modification of both.
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