# 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, ).
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, ).