Bayesian Causal Inference: A Critical Review

TL;DR

This paper critically reviews Bayesian causal inference, discussing estimands, assumptions, priors, and complex mechanisms, highlighting unique issues and the importance of design and overlap in causal analysis.

Contribution

It provides a comprehensive critique of Bayesian causal inference, emphasizing issues like propensity scores, priors, and complex treatments, which are less explored in prior literature.

Findings

Bayesian causal inference faces unique challenges with priors and identifiability.

Covariate overlap and design are crucial for valid Bayesian causal estimates.

Extensions to instrumental variables and time-varying treatments are discussed.

Abstract

This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, identification assumptions, the general structure of Bayesian inference of causal effects, and sensitivity analysis. We highlight issues that are unique to Bayesian causal inference, including the role of the propensity score, definition of identifiability, the choice of priors in both low and high dimensional regimes. We point out the central role of covariate overlap and more generally the design stage in Bayesian causal inference. We extend the discussion to two complex assignment mechanisms: instrumental variable and time-varying treatments. Throughout, we illustrate the key concepts via examples.