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August 2023 The Role of Exchangeability in Causal Inference
Olli Saarela, David A. Stephens, Erica E. M. Moodie
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Statist. Sci. 38(3): 369-385 (August 2023). DOI: 10.1214/22-STS879


Though the notion of exchangeability has been discussed in the causal inference literature under various guises, it has rarely taken its original meaning as a symmetry property of probability distributions. As this property is a standard component of Bayesian inference, we argue that in Bayesian causal inference it is natural to link the causal model, including the notion of confounding and definition of causal contrasts of interest, to the concept of exchangeability. Here, we propose a probabilistic between-group exchangeability property as an identifying condition for causal effects, relate it to alternative conditions for unconfounded inferences (commonly stated using potential outcomes) and define causal contrasts in the presence of exchangeability in terms of posterior predictive expectations for further exchangeable units. While our main focus is on a point treatment setting, we also investigate how this reasoning carries over to longitudinal settings.


The authors would like to thank an anonymous reviewer and the Editor for their thorough and constructive feedback that helped us to sharpen and solidify our argument. The first author would like to thank Professor Dennis Lindley (1923–2013) for the inspiration for this work and for hosting him and Professor Elja Arjas in Minehead in April 2012.


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Olli Saarela. David A. Stephens. Erica E. M. Moodie. "The Role of Exchangeability in Causal Inference." Statist. Sci. 38 (3) 369 - 385, August 2023.


Published: August 2023
First available in Project Euclid: 20 August 2023

MathSciNet: MR4630374
Digital Object Identifier: 10.1214/22-STS879

Keywords: Bayesian inference , Causal inference , confounding , exchangeability , posterior predictive inference

Rights: Copyright © 2023 Institute of Mathematical Statistics

Vol.38 • No. 3 • August 2023
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