Bayesian Additive Regression Trees (BART) has been shown to be an effective framework for modeling nonlinear regression functions, with strong predictive performance in a variety of contexts. The BART prior over a regression function is defined by independent prior distributions on tree structure and leaf or end-node parameters. We consider two flavors of BART. First, BART with Targeted Smoothing induces smoothness over a single covariate by replacing independent Gaussian leaf priors with smooth functions. Second, Bayesian Causal Forests (BCF) has successfully adapted BART for estimating heterogeneous treatment effects from observational data, particularly in cases where standard methods yield biased estimates due to strong confounding. BCF parameterizes BART models to allow for separate regularization of the treatment and prognostic effects, making it possible to shrink towards homogeneity.
We introduce a new version of the BCF prior which incorporates targeted smoothing for modeling heterogeneous treatment effects which vary smoothly over a target covariate. We demonstrate the utility of this approach by applying our model to a timely women's health problem: comparing two d