Bayesian Inference for Causal Effects: The Role of Randomization
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Causal Question / Estimand
Causal effects are comparisons among the Potential-Outcomes that would be observed under all possible treatment assignments; only one assignment is realized, so the others are missing. The target is the average Causal-Estimand, obtained from the predictive distribution of the unobserved outcomes.
Identification Strategy
A Bayesian formulation: inference for causal effects follows from finding the predictive distribution of the missing potential outcomes. This makes the sampling, assignment, and recording mechanisms central. Unless these mechanisms are ignorable (known probabilistic functions of recorded values), the analyst must model them, and inferences become sensitive to the prior. Randomization is the assignment mechanism that keeps a valid Bayesian analysis insensitive to prior specification.
Key Assumptions
Ignorability — given its precise mechanism-level meaning here (“ignorable” = known probabilistic function of recorded values) — plus Potential-Outcomes and Randomization.
Threats to Validity
Non-ignorable assignment/sampling mechanisms force explicit modeling and leave causal conclusions sensitive to the prior. Rubin also notes that not all ignorable mechanisms yield prior-insensitive inferences — randomized designs are special in doing so.
Setting / Data
n/a — theoretical/methodological. Aspirin-and-headache thought experiment as the canonical illustration of the unobservable counterfactual.
Key Claims
- Provides the Bayesian foundation for causal inference via the predictive distribution of missing potential outcomes (the missing-data view).
- Defines ignorable assignment/sampling mechanisms and shows why they matter.
- Argues randomization plays a central role even in Bayesian inference: randomized studies are substantially easier to analyze than comparable nonrandomized ones, rebutting Bayesian opponents of randomization.
Connections
- Builds on: Rubin1974-EstimatingCausalEffects
- See also: Rubin1977-AssignmentOnCovariate, Rubin1980-RandomizationAnalysis, Holland1986-StatisticsAndCausalInference, Foundations
Citation
Rubin, D. B. (1978). Bayesian Inference for Causal Effects: The Role of Randomization. The Annals of Statistics, 6(1), 34–58.