Bayesian Causal Inference
Routing Summary
This folder covers Bayesian and ML-based causal inference. Contains 39 notes across 7 sub-topics.
- For potential outcomes setup, SUTVA, ignorability, propensity score? → Foundations
- For Bayesian CI likelihood factorization, BART/GP/BCF outcome models, propensity score strategies? → Bayesian Inference
- For sensitivity analysis (E-value, copula), IV/principal stratification, time-varying treatments? → Sensitivity and Complex Mechanisms
- For interactive and LLM-based methods to elicit causal structure? → Knowledge Elicitation
- For S/T/X-learners and CATE estimation with ML? → Treatment Effect Estimation
- For Bayesian structural time-series and CausalImpact? → Time Series Causal Inference
- For optimal dynamic treatment regimes (sequential decisions, Q-learning, A-learning)? → Dynamic Treatment Regimes
- For paper overview of Li et al. 2022? → Li et al 2022 - Overview
Sub-topics
| Sub-topic | Notes | Domain |
|---|---|---|
| Foundations | 3 | Potential outcomes, SUTVA, ignorability, causal estimands, frequentist methods |
| Bayesian Inference | 3 | Bayesian CI structure, outcome models (BART/GP/BCF), propensity score strategies |
| Sensitivity and Complex Mechanisms | 3 | E-value, copula sensitivity, IV/principal stratification, g-formula, time-varying treatments |
| Knowledge Elicitation | 9 | Interactive (Yamashita 2020) and LLM-based (Shaposhnyk 2025) causal structure elicitation |
| Treatment Effect Estimation | 6 | S/T/X-learner metalearners for CATE; minimax rates; voter turnout & transphobia applications |
| Time Series Causal Inference | 7 | BSTS model; spike-and-slab; Gibbs sampler; CausalImpact; advertising application |
| Dynamic Treatment Regimes | 5 | Optimal multi-stage treatment rules; potential-outcomes framework; backward induction (Q/value functions); Q-learning; A-learning, g-estimation & double robustness (Schulte, Tsiatis, Laber & Davidian 2014) |
Paper Overview
- Li et al 2022 - Overview — “Bayesian causal inference: a critical review”, Li, Ding & Mealli (2022), Phil. Trans. R. Soc. A 381
- Yamashita 2020 - Overview — “Interactive method to elicit local causal knowledge”, Yamashita et al. (2020), HCII 2020
- Shaposhnyk 2025 - Overview — “Can LLMs assist expert elicitation for probabilistic causal modeling?”, Shaposhnyk et al. (2025), arXiv
- Künzel 2019 - Overview — “Metalearners for estimating heterogeneous treatment effects”, Künzel et al. (2019), PNAS 116(10)
- Brodersen 2015 - Overview — “Inferring causal impact using Bayesian structural time-series models”, Brodersen et al. (2015), Ann. Appl. Stat. 9(1)
Key Concept Dependency Chain
Potential Outcomes Framework
└─► Causal Estimands (ITE, SATE, CATE, PATE, MATE)
└─► Frequentist Causal Estimation (IPW, DR, matching)
└─► Metalearners for CATE [Künzel 2019]
├── S-Learner (single model)
├── T-Learner (separate models; minimax rate)
└── X-Learner (cross-imputation; optimal for unbalanced groups)
└─► General Structure of Bayesian CI (factorization, Assumption 3.2)
└─► Bayesian Outcome Models (BART, BCF, GP, regularization-induced confounding)
└─► Propensity Score in Bayesian CI (3 strategies)
└─► Sensitivity Analysis in Observational Studies (E-value, copula)
└─► Instrumental Variables and Principal Stratification (CACE, compliance strata)
└─► Time-Varying Treatments and G-computation (g-formula, sequential ignorability)
└─► Counterfactual Inference [Brodersen 2015]
└─► Bayesian Structural Time-Series Model (BSTS)
├── Local Linear Trend + Seasonality
├── Spike-and-Slab Prior (variable selection)
├── MCMC Inference (Gibbs + Kalman smoother)
└── Counterfactual Impact Estimation (pointwise, cumulative, running avg)
Causal Structure Learning
└─► Knowledge Elicitation [Yamashita 2020]
├── Cause-Precondition-Effect Model
├── Interactive GUI Workshop Method
└── NLP Causal Extraction (Method A + B, Word2Vec)
└─► LLM Expert Elicitation [Shaposhnyk 2025]
├── Dual-LLM Architecture (GPT-4o + Claude)
├── BN Construction Comparison (LLM vs BIC vs Human)
└── Entropy-Based BN Evaluation
Cross-Cutting Themes
- Propensity score paradox: Drops from Bayesian likelihood under ignorability, yet essential for design/overlap — appears in General Structure of Bayesian CI, Propensity Score in Bayesian CI, Bayesian Outcome Models
- Regularization-induced confounding: In high dimensions, standard Bayesian priors can bias causal estimates — see ^warn-reg-confounding and ^warn-prior-dogmatism
- Transparent parametrization: Separating identifiable from non-identifiable parameters — see Sensitivity Analysis in Observational Studies, General Structure of Bayesian CI
Sources
- Li et al. - 2022 - Bayesian causal inference a critical review.pdf — Li F, Ding P, Mealli F. 2023. Phil. Trans. R. Soc. A 381: 20220153
- Yamashita et al. - 2020 - Interactive Method to Elicit Local Causal Knowledge for Creating a Huge Causal Network.pdf — Yamashita G, Kanno T, Furuta K. 2020. HCII, LNCS 12217, pp. 437-446
- Shaposhnyk et al. - 2025 - Can LLMs Assist Expert Elicitation for Probabilistic Causal Modeling.pdf — Shaposhnyk O, Zahorska D, Yanushkevich S. 2025. arXiv:2504.10397
- Künzel et al. - 2017 - Metalearners for estimating heterogeneous treatment effects using machine learning.pdf — Künzel SR, Sekhon JS, Bickel PJ, Yu B. 2019. PNAS 116(10): 4156-4165
- Brodersen - 2015 - Inferring causal impact using Bayesian structural time-series models.pdf — Brodersen KH, Gallusser F, Koehler J, Remy N, Scott SL. 2015. Ann. Appl. Stat. 9(1): 247-274
- q- and a- learning.pdf — Schulte PJ, Tsiatis AA, Laber EB, Davidian M. 2014. “Q- and A-learning Methods for Estimating Optimal Dynamic Treatment Regimes”, Statistical Science 29(4): 640-661
Cross-Links to Existing Vault Notes
- Bayesian Propensity Scores and IPW — Bayesian IPW via Liao-Zigler two-stage method (Heiss blog) — related to Propensity Score in Bayesian CI Strategy 3
- Nonparametric Causal Inference — BART and non-parametric Bayesian causal methods — related to Bayesian Outcome Models
- Copula Estimation — copula methods used in sensitivity analysis — related to Sensitivity Analysis in Observational Studies