The Annals of Statistics

Bayesian Inference for Causal Effects: The Role of Randomization

Donald B. Rubin

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Causal effects are comparisons among values that would have been observed under all possible assignments of treatments to experimental units. In an experiment, one assignment of treatments is chosen and only the values under that assignment can be observed. Bayesian inference for causal effects follows from finding the predictive distribution of the values under the other assignments of treatments. This perspective makes clear the role of mechanisms that sample experimental units, assign treatments and record data. Unless these mechanisms are ignorable (known probabilistic functions of recorded values), the Bayesian must model them in the data analysis and, consequently, confront inferences for causal effects that are sensitive to the specification of the prior distribution of the data. Moreover, not all ignorable mechanisms can yield data from which inferences for causal effects are insensitive to prior specifications. Classical randomized designs stand out as especially appealing assignment mechanisms designed to make inference for causal effects straightforward by limiting the sensitivity of a valid Bayesian analysis.

Article information

Ann. Statist., Volume 6, Number 1 (1978), 34-58.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62A15
Secondary: 62B15: Theory of statistical experiments 62C10: Bayesian problems; characterization of Bayes procedures 62F15: Bayesian inference 62K99: None of the above, but in this section

Bayesian inference randomization causality missing data experimentation


Rubin, Donald B. Bayesian Inference for Causal Effects: The Role of Randomization. Ann. Statist. 6 (1978), no. 1, 34--58. doi:10.1214/aos/1176344064.

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