Search for: All records

Abstract 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 semicontinuous responses. In this paper, we present a 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‐toward‐homoskedasticity” prior and a gamma hurdle model. 

Bayesian additive regression trees (BART) provides a flexible approach to fitting a variety of regression models while avoiding strong parametric assumptions. The sum-of-trees model is embedded in a Bayesian inferential framework to support uncertainty quantification and provide a principled approach to regularization through prior specification. This article presents the basic approach and discusses further development of the original algorithm that supports a variety of data structures and assumptions. We describe augmentations of the prior specification to accommodate higher dimensional data and smoother functions. Recent theoretical developments provide justifications for the performance observed in simulations and other settings. Use of BART in causal inference provides an additional avenue for extensions and applications. We discuss software options as well as challenges and future directions.