# Bayesian Additive Regression Trees With Parametric Models of Heteroskedasticity

arXiv: https://arxiv.org/abs/1402.5397 · HTML: https://mlsanity.com/paper/1402.5397/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2014.

## Built on by (most cited first, 2 of 2)

- [Sharded Bayesian Additive Regression Trees](https://mlsanity.com/paper/2306.00361/) (2023)
- [SoftBart: Soft Bayesian Additive Regression Trees](https://mlsanity.com/paper/2210.16375/) (2022)

## Abstract (arXiv)

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.