Semiparametric Bayesian causal inference

Abstract

We develop a semiparametric Bayesian approach for estimating the mean\nresponse in a missing data model with binary outcomes and a nonparametrically\nmodelled propensity score. Equivalently we estimate the causal effect of a\ntreatment, correcting nonparametrically for confounding. We show that standard\nGaussian process priors satisfy a semiparametric Bernstein-von Mises theorem\nunder smoothness conditions. We further propose a novel propensity\nscore-dependent prior that provides efficient inference under strictly weaker\nconditions. We also show that it is theoretically preferable to model the\ncovariate distribution with a Dirichlet process or Bayesian bootstrap, rather\nthan modelling the covariate density using a Gaussian process prior.\n