  This paper demonstrates the advantages of sharing information about unknown
features of covariates across multiple model components in various
nonparametric regression problems including multivariate, heteroscedastic, and
semi-continuous responses. In this paper, we present methodology which allows
for information to be shared nonparametrically across various model components
using Bayesian sum-of-tree models. Our simulation results demonstrate that
sharing of information across related model components is often very
beneficial, particularly in sparse high-dimensional problems in which variable
selection must be conducted. We illustrate our methodology by analyzing medical
expenditure data from the Medical Expenditure Panel Survey (MEPS). To
facilitate the Bayesian nonparametric regression analysis, we develop two novel
models for analyzing the MEPS data using Bayesian additive regression trees - a
heteroskedastic log-normal hurdle model with a
"shrink-towards-homoskedasticity" prior, and a gamma hurdle model.
