Priors and Propensity Scores in Bayesian Causal Inference

Aronow et al. (2025) provide a convincing case for the special status of randomized controlled trials (RCTs) in which the propensity scores are known and can be used to make causal inferences. Here we provide a Bayesian perspective on their work by summarizing recent developments in the Bayesian literature on the topic. Whether the propensity score should play a role in Bayesian causal inference - and what that role(s) should be - has been a controversial topic for some time. We begin by describing Bayesian inference for population-level estimands and show that under commonly made (but not necessarily required) assumptions, the propensity score model has no role to play in Bayesian causal inference from a purist perspective. We discuss recent work on why these assumptions can be problematic - particularly in high-dimensional models - and discuss several Bayesian motivations for relaxing them. We describe out recent approaches for incorporating the propensity score correspond to di erent ways of relaxing these assumptions. Given these considerations, we illustrate how a Bayesian might approach the synethic examples of Aronow et al. (2025).