Bayesian Trees for Conditional Mean and Variance
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, <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, <10.1214>).10.1214>1709.07542v2>