Causal inference under mis-specification: adjustment based on the propensity score

TL;DR

This paper develops fully Bayesian methods for causal inference using propensity scores, addressing model mis-specification issues with decision-theoretic and bootstrap-based approaches.

Contribution

It introduces a novel Bayesian framework for propensity score regression that accounts for model mis-specification through decision-theoretic loss minimization and Bayesian bootstrap techniques.

Findings

Bayesian bootstrap approach shows good frequentist properties.

Decision-theoretic methods enable valid Bayesian inference under mis-specification.

Proposed methods improve robustness of causal inference in practice.

Abstract

We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional `likelihood times prior' posterior inference; in addition, most methods rely on parametric and distributional assumptions, and presumed correct specification. We emphasize that causal inference is typically carried out in settings of mis-specification, and develop strategies for fully Bayesian inference that reflect this. We focus on methods based on decision-theoretic arguments, and show how inference based on loss-minimization can give valid and fully Bayesian inference. We propose a computational approach to inference based on the Bayesian bootstrap which has good Bayesian and frequentist properties.