Causal Inference in the Bayesian Framework: Principles and Applications
Mengli Wang · Asian Journal of Probability and Statistics · 2025
Causal inference is fundamental to scientific inquiry, yet its methodologies often lack a cohesive probabilistic framework. While the U.S. FDA advocates for Bayesian methods in drug development, their potential to unify and advance causal inference remains underexplored. This study addresses this gap by formalizing a Bayesian framework for causal inference, which provides a principled mechanism to integrate prior evidence and quantify full uncertainty in causal estimates. We delineate the theoretical underpinnings of this approach and demonstrate its practical utility through a numerical example. This framework not only calculates the posterior distribution of causal hypotheses, but also provides a method different from traditional hypothesis testing, advancing the methodology by better adapting to complex data structures and prior knowledge.