# Bayesian Causal Inference: A Critical Review

arXiv: https://arxiv.org/abs/2206.15460 · HTML: https://mlsanity.com/paper/2206.15460/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2022.

## Built on by (most cited first, 21 of 21)

- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confounding](https://mlsanity.com/paper/2306.09520/) (2023)
- [An AI-powered Bayesian generative modeling approach for causal inference in observational studies](https://mlsanity.com/paper/2501.00755/) (2025)
- [Bayesian Safe Policy Learning with Chance Constrained Optimization: Application to Military Security Assessment during the Vietnam War](https://mlsanity.com/paper/2307.08840/) (2023)
- [Uncertainty Quantification in Heterogeneous Treatment Effect Estimation with Gaussian-Process-Based Partially Linear Model](https://mlsanity.com/paper/2312.10435/) (2023)
- [Causal Foundation Models with Continuous Treatments](https://mlsanity.com/paper/2605.15133/) (2026)
- [Causal-EPIG: A Prediction-Oriented Active Learning Framework for CATE Estimation](https://mlsanity.com/paper/2509.21866/) (2025)
- [A Forecaster's Review of Judea Pearl's Causality: Models, Reasoning and Inference, Second Edition, 2009](https://mlsanity.com/paper/2308.05451/) (2023)
- [A flexible Bayesian g-formula for causal survival analyses with time-dependent confounding](https://mlsanity.com/paper/2402.02306/) (2024)
- [Bayesian Estimation of Causal Effects Using Proxies of a Latent Interference Network](https://mlsanity.com/paper/2505.08395/) (2025)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [Bayesian Semiparametric Causal Inference: Targeted Doubly Robust Estimation of Treatment Effects](https://mlsanity.com/paper/2511.15904/) (2025)
- [Retrospective Counterfactual Prediction by Conditioning on the Factual Outcome: A Cross-World Approach](https://mlsanity.com/paper/2603.27320/) (2026)
- [Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap](https://mlsanity.com/paper/2301.05703/) (2023)
- [Individualized Multi-Treatment Response Curves Estimation using RBF-net with Shared Neurons](https://mlsanity.com/paper/2401.16571/) (2024)
- [Improving Generative Methods for Causal Evaluation via Simulation-Based Inference](https://mlsanity.com/paper/2509.02892/) (2025)
- [Bayesian Supervised Causal Clustering](https://mlsanity.com/paper/2603.05288/) (2026)
- [Bayesian Sensitivity of Causal Inference Estimators under Evidence-Based Priors](https://mlsanity.com/paper/2605.07993/) (2026)
- [Some cautionary tales about Bayesian predictive inference](https://mlsanity.com/paper/2607.19206/) (2026)
- [AI Deployment Accountability Engineering: A Vision for Accountable AI in Safety-Critical Socio-Technical Systems](https://mlsanity.com/paper/2609.14592/) (2026)

## Abstract (arXiv)

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.