Christoph Breunig, Ruixuan Liu, Zhengfei Yu
arXiv 29 Sep 2025 · Statistics — Methodology
arXiv:2509.24634 · PDF · DOI · OpenAlex · Extracted main text
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Yiu, A., Fong, E., Holmes, C., and Rousseau, J (2025) Semiparametric posterior corrections | 0.941 | 18 | 8 | 83% |
| 2 | Rocková, V. and van der Pas, S (2020) Posterior concentration for bayesian regression trees and forests | 0.928 | 5 | 3 | 80% |
| 3 | Ray, K. and van der Vaart, A (2020) Semiparametric bayesian causal inference | 0.885 | 13 | 7 | 69% |
| 4 | Linero, A. R. and Yang, Y (2018) Bayesian regression tree ensembles that adapt to smoothness and sparsity | 0.874 | 6 | 2 | 100% |
| 5 | Breunig, C., Liu, R., and Yu, Z (2025) Double robust bayesian inference on average treatment effects self | 0.843 | 15 | 4 | 60% |
| 6 | van der Vaart, A. and Wellner, J. A (1996) Weak convergence and empirical processes | 0.754 | 7 | 4 | 43% |
| 7 | Chipman, H. A., George, E. I., and McCulloch, R. E (2010) Bart: Bayesian additive regression trees | 0.737 | 4 | 3 | 50% |
| 8 | Ghosal, S., Ghosh, J. K., and van der Vaart, A. W (2000) Convergence rates of posterior distributions | 0.737 | 3 | 3 | 67% |
| 9 | Jeong, S. and Rocková, V (2023) The art of bart: Minimax optimality over nonhomogeneous smoothness in high dimension | 0.727 | 13 | 3 | 38% |
| 10 | Sparapani, R., Spanbauer, C., and McCulloch, R (2021) Nonparametric machine learning and efficient computation with bayesian additive regression trees: The bart r package | 0.693 | 6 | 3 | 33% |
Showing the top 10 of 40 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Debiased Bayesian Inference for High-dimensional Regression Models | 0.405 | 1 | 1 |