Bayesian causal inference: a critical review.

Area of Science:

• Statistics
• Causal Inference
• Bayesian Methods

Background:

• The potential outcomes framework is a cornerstone of causal inference.
• Bayesian methods offer a probabilistic approach to quantifying uncertainty in causal effect estimation.
• Understanding the nuances of Bayesian causal inference is crucial for robust scientific conclusions.

Purpose of the Study:

• To critically review the Bayesian perspective of causal inference using the potential outcomes framework.
• To identify and discuss issues unique to Bayesian causal inference.
• To extend the discussion to complex assignment mechanisms and illustrate concepts with examples.

Main Methods:

• Review of causal estimands and assignment mechanisms.
• Examination of Bayesian inference structure for causal effects.
• Analysis of sensitivity analysis in Bayesian causal inference.
• Discussion of propensity scores, identifiability, and prior choices.

Main Results:

• Identified unique challenges in Bayesian causal inference, including prior selection and identifiability.
• Highlighted the critical role of covariate overlap and study design.
• Extended the framework to instrumental variables and time-varying treatments.
• Provided a balanced view of the strengths and weaknesses of the Bayesian approach.

Conclusions:

• Bayesian causal inference offers a comprehensive framework for estimating causal effects.
• Careful consideration of study design, prior specification, and sensitivity analysis is paramount.
• The Bayesian approach provides valuable tools for complex causal inference problems.