SEMIPARAMETRIC BAYESIAN CAUSAL INFERENCE

• 成果类型: Article
• 署名作者: Ray, Kolyan; van der Vaart, Aad
• 署名单位: Imperial College London; Leiden University; Leiden University - Excl LUMC
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1919
• 发表日期: 2020
• 页码: 2999-3020
• 关键词: von-mises theorem; posterior distributions; propensity score; models; rates; contraction; functionals; INFORMATION; regression; EFFICIENCY

摘要

We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently, we estimate the causal effect of a treatment, correcting nonparametrically for confounding. We show that standard Gaussian process priors satisfy a semiparametric Bernsteinvon Mises theorem under smoothness conditions. We further propose a novel propensity score-dependent prior that provides efficient inference under strictly weaker conditions. We also show that it is theoretically preferable to model the covariate distribution with a Dirichlet process or Bayesian bootstrap, rather than modelling its density.