Tree-Based Bayesian Treatment Effect Analysis

Abstract: The inclusion of the propensity score as a covariate in Bayesian regression trees for causal inference can reduce the bias in treatment effect estimations, which occurs due to the regularization-induced confounding phenomenon. This study advocate for the use of the propensity score by evaluating it under a full-Bayesian variable selection setting, and the use of Individual Conditional Expectation Plots, which is a graphical tool that can improve treatment effect analysis on tree-based Bayesian models and others "black box" models. The first one, even if poorly estimated, can lead to bias reduction on the estimated treatment effects, while the latter can be used to found groups of individuals which have different responses to the applied treatment, and analyze the impact of each variable in the estimated treatment effect.