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Robust Semiparametric Inference for Bayesian Additive Regression Trees

Christoph Breunig, Ruixuan Liu, Zhengfei Yu

arXiv 29 Sep 2025 · Statistics — Methodology

arXiv:2509.24634 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

40
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136
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Yiu, A., Fong, E., Holmes, C., and Rousseau, J (2025) Semiparametric posterior corrections0.94118883%
2Rocková, V. and van der Pas, S (2020) Posterior concentration for bayesian regression trees and forests0.9285380%
3Ray, K. and van der Vaart, A (2020) Semiparametric bayesian causal inference0.88513769%
4Linero, A. R. and Yang, Y (2018) Bayesian regression tree ensembles that adapt to smoothness and sparsity0.87462100%
5Breunig, C., Liu, R., and Yu, Z (2025) Double robust bayesian inference on average treatment effects self0.84315460%
6van der Vaart, A. and Wellner, J. A (1996) Weak convergence and empirical processes0.7547443%
7Chipman, H. A., George, E. I., and McCulloch, R. E (2010) Bart: Bayesian additive regression trees0.7374350%
8Ghosal, S., Ghosh, J. K., and van der Vaart, A. W (2000) Convergence rates of posterior distributions0.7373367%
9Jeong, S. and Rocková, V (2023) The art of bart: Minimax optimality over nonhomogeneous smoothness in high dimension0.72713338%
10Sparapani, R., Spanbauer, C., and McCulloch, R (2021) Nonparametric machine learning and efficient computation with bayesian additive regression trees: The bart r package0.6936333%

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Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Debiased Bayesian Inference for High-dimensional Regression Models0.40511