The central role of Bayes theorem for joint estimation of causal effects and propensity scores

TL;DR

This paper explores the fundamental role of Bayes theorem in the joint estimation of causal effects and propensity scores, highlighting the conceptual tensions and providing clarity for future Bayesian causal inference methods.

Contribution

It clarifies the implicit discord between propensity score methods and Bayesian inference, offering insights into their integration for causal effect estimation.

Findings

Identifies a fundamental tension between propensity scores and Bayesian methods.

Provides a conceptual framework for Bayesian causal effect estimation.

Clarifies the role of Bayes theorem in propensity score analysis.

Abstract

Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal effects. Underlying this recent body of literature on Bayesian propensity score estimation is an implicit discordance between the goal of the propensity score and the use of Bayes theorem. The propensity score condenses multivariate covariate information into a scalar to allow estimation of causal effects without specifying a model for how each covariate relates to the outcome. Avoiding specification of a detailed model for the outcome response surface is valuable for robust estimation of causal effects, but this strategy is at odds with the use of Bayes theorem, which presupposes a full probability model for the observed data. The goal of this paper is to explicate this fundamental feature of Bayesian estimation of causal effects with propensity scores in order to provide context for the existing literature and for future work on this important topic.