Bayesian Regression Trees, Nonparametric Heteroscedastic Regression Modeling and MCMC Sampling
Bayesian additive regression trees (BART) have become increasingly popular as flexible and scalable non-parametric models useful in many modern applied statistics regression problems. They bring many advantages to the practitioner dealing with large datasets and complex non-linear response surfaces, such as the matrix-free formulation and the lack of a requirement to specify a regression basis a priori. However, there are some known challenges to this modeling approach, such as poor mixing of the MCMC sampler and inappropriate uncertainty intervals when the assumed homoscedastic variance model is violated. In this talk, we introduce a new Bayesian regression tree model that allows for possible heteroscedasticity in the variance model and devise novel MCMC samplers that appear to adequately explore the posterior tree space of this model.