Semiparametric Bayesian causal inference

TL;DR

This paper introduces a semiparametric Bayesian method for causal inference with binary outcomes, utilizing Gaussian process and propensity score-dependent priors to improve estimation under weaker assumptions.

Contribution

It develops a novel Bayesian approach that combines Gaussian process priors and propensity score-dependent priors for more efficient causal effect estimation.

Findings

Gaussian process priors satisfy a Bernstein-von Mises theorem under smoothness.

Propensity score-dependent priors offer efficient inference under weaker conditions.

Modeling covariate distribution with Dirichlet process is theoretically preferable.

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 the covariate density using a Gaussian process prior.