Priors and Propensity Scores in Bayesian Causal Inference.

Area of Science:

• Statistics
• Causal Inference
• Bayesian Methods

Background:

• Randomized controlled trials (RCTs) are crucial for causal inference.
• The role of propensity scores in Bayesian causal inference remains a debated topic.
• High-dimensional models can challenge standard assumptions in causal inference.

Purpose of the Study:

• To provide a Bayesian perspective on the use of propensity scores in causal inference, building on Aronow et al. (2025).
• To explore the controversial role of propensity scores within Bayesian causal inference frameworks.
• To present recent Bayesian approaches for incorporating propensity scores by relaxing conventional assumptions.

Main Methods:

• Review of Bayesian literature on propensity scores and causal inference.
• Description of Bayesian inference for population-level estimands.
• Illustration of Bayesian approaches using synthetic examples from Aronow et al. (2025).

Main Results:

• Under standard assumptions, propensity score models may not be necessary for Bayesian causal inference.
• Relaxing these assumptions, particularly in high-dimensional settings, provides motivations for using propensity scores.
• Recent Bayesian methods offer ways to incorporate propensity scores by adjusting underlying assumptions.

Conclusions:

• The utility of propensity scores in Bayesian causal inference depends on the specific assumptions made.
• Bayesian methods can accommodate propensity scores through various strategies for relaxing restrictive assumptions.
• This work offers a framework for applying Bayesian causal inference with propensity scores in complex scenarios.