{"ID":2863517,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.24634","arxiv_id":"2509.24634","title":"Robust Semiparametric Inference for Bayesian Additive Regression Trees","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.","short_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-dimensi...","url_abs":"https://arxiv.org/abs/2509.24634","url_pdf":"https://arxiv.org/pdf/2509.24634v2","authors":"[\"Christoph Breunig\",\"Ruixuan Liu\",\"Zhengfei Yu\"]","published":"2025-09-29T11:42:06Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"econ.EM\",\"math.ST\"]","methods":"[]","has_code":false}