BART for Causal Inference

Estimating a treatment effect — did a new margin policy actually reduce failed trades, controlling for everything else that changed at the same time? — usually starts with a linear regression, which forces the relationship between covariates and outcome into a straight line even when the truth is curved or interacts in complicated ways. BART (Bayesian Additive Regression Trees) instead sums up many small, shallow regression trees, each capturing a little piece of the relationship, with a Bayesian prior that keeps each individual tree deliberately weak so no single tree dominates and the ensemble stays smooth rather than overfitting the training data.

For causal inference specifically, BART is fit on the outcome as a function of both the treatment indicator and the covariates, letting the treatment effect vary flexibly across different types of units without the analyst having to specify interaction terms by hand — a client with a small book might respond very differently to the margin policy than a large institutional account, and BART can pick that up without being told to look for it.

Because it's Bayesian, BART naturally produces a posterior distribution over the estimated treatment effect for each unit, rather than just a point estimate, giving a built-in credible interval that reflects genuine estimation uncertainty. This is one reason BART became a standard baseline in causal inference competitions and applied economics: it combines tree-based flexibility with honest uncertainty quantification in one model.