October 20, 2025Open Access

Robust Semiparametric Inference for Bayesian Additive Regression Trees

CBChristoph BreunigUniversity of Bonn RLRuixuan LiuUniversity of Southern California ZYZhengfei YuOsaka University of Economics

Key Points

The new RoBART method addresses bias in Bayesian Additive Regression Trees, improving inference accuracy.
Monte Carlo studies show reduced bias and improved coverage when using RoBART compared to existing methods.
Non-smoothness of BART complicates asymptotic theory, necessitating a robust inference framework.
A new Bernstein-von Mises theorem is established, revealing a bias term in the limit distribution.

Abstract

We develop a semiparametric framework for inference on the mean response in missing-data settings using a corrected posterior distribution. Our approach is tailored to Bayesian Additive Regression Trees (BART), which is a powerful predictive method but whose nonsmoothness complicate asymptotic theory with multi-dimensional covariates. When using BART combined with Bayesian bootstrap weights, we establish a new Bernstein-von Mises theorem and show that the limit distribution generally contains a bias term. To address this, we introduce RoBART, a posterior bias-correction that robustifies BART for valid inference on the mean response. Monte Carlo studies support our theory, demonstrating reduced bias and improved coverage relative to existing procedures using BART.

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