Open Access
October 2020 Semiparametric Bayesian causal inference
Kolyan Ray, Aad van der Vaart
Ann. Statist. 48(5): 2999-3020 (October 2020). DOI: 10.1214/19-AOS1919


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.


Download Citation

Kolyan Ray. Aad van der Vaart. "Semiparametric Bayesian causal inference." Ann. Statist. 48 (5) 2999 - 3020, October 2020.


Received: 1 August 2018; Revised: 1 August 2019; Published: October 2020
First available in Project Euclid: 19 September 2020

MathSciNet: MR4152632
Digital Object Identifier: 10.1214/19-AOS1919

Primary: 62G20
Secondary: 62G08 , 62G15

Keywords: Bernstein–Von Mises , Causal inference , Dirichlet process , Gaussian processes , propensity score-dependent priors

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 5 • October 2020
Back to Top