Semiparametric posterior corrections

• 成果类型: Article
• 署名作者: Yiu, Andrew; Fong, Edwin; Holmes, Chris; Rousseau, Judith
• 署名单位: University of Oxford; University of Hong Kong; University of Oxford; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf005
• 发表日期: 2025
• 页码: 1025-1054
• 关键词: von mises theorem; bayesian density-estimation; it-yourself methods; Causal Inference; frequentist properties; integral functionals; efficient estimation; convergence-rates; ORDER; statistics

摘要

We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization, and predictive power of nonparametric Bayesian procedures to estimate low-dimensional functionals of interest without being restricted by the holistic Bayesian formalism. Starting from a conventional posterior on the whole data-generating distribution, we correct the marginal posterior for each functional of interest with the help of the Bayesian bootstrap. We provide conditions for the resulting one-step posterior to possess calibrated frequentist properties and specialize the results for several canonical examples: the integrated squared density, the mean of a missing-at-random outcome, and the average causal treatment effect on the treated. The procedure is computationally attractive, requiring only a simple, efficient postprocessing step that can be attached onto any arbitrary posterior sampling algorithm. Using the ACIC 2016 causal data analysis competition, we illustrate that our approach can outperform the existing state-of-the-art through the propagation of Bayesian uncertainty.