A model of the form Y = f(x) + s(x) Z is fit where functions f and s are modeled with ensembles of trees and Z is standard normal. This model is developed in the paper 'Heteroscedastic BART Via Multiplicative Regression Trees' (Pratola, Chipman, George, and McCulloch, 2019, <arXiv:1709.07542v2>). BART refers to Bayesian Additive Regression Trees. See the R-package 'BART'. The predictor vector x may be high dimensional. A Markov Chain Monte Carlo (MCMC) algorithm provides Bayesian posterior uncertainty for both f and s. The MCMC uses the recent innovations in Efficient Metropolis--Hastings proposal mechanisms for Bayesian regression tree models (Pratola, 2015, Bayesian Analysis, <doi:10.1214/16-BA999>).
