Semiparametric Bayesian causal inference
The Annals of Statistics · 2020 · Volume 48 · Issue 5
Abstract
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 its density.
Keywords
62G08, 62G15, 62G20, Bernstein–Von Mises, Causal inference, Dirichlet process, Gaussian processes, propensity score-dependent priors
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