2018/08/31 by Kolyan Ray, Aad van der Vaart · 1 citation
Mathematics · #math.ST #stat.ME #stat.TH #msc:62G20 #msc:62G15 #msc:62G08
paper · pdf · doi:10.1214/19-aos1919
published as Ann. Statist. 48 (2020), 2999-3020 · 54 pages
arxiv created 2019/10/10 · arxiv updated 2020/09/23
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 Bernstein-von 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 the covariate density using a Gaussian process prior.