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Exchangeability and Data Analysis

Author

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  • David Draper
  • James S. Hodges
  • Colin L. Mallows
  • Daryl Pregibon

Abstract

The term ‘exchangeability’ was introduced by de Finetti in the context of personal probability to describe a particular sense in which quantities treated as random variables in a probability specification are thought to be similar. We believe, however, that judgments of similarity are more primitive than those of probability and are at the heart of all statistical activities, including those for which probability specifications are absent or contrived. In this paper, we give a definition of exchangeability in a descriptive context, which extends de Finetti's concept to a wider domain. Our objective is to analyse the logic of judgments of exchangeability (or similarity, or homogeneity), to clarify the roles of context and data analysis in these judgments. We give several examples to illustrate the nature of these judgments in description, inference and prediction. We use this discussion to clarify the extent to which judgments of similarity in inference and prediction can be based on data, and the extent to which they must rely on pure faith. Our discussion is a contribution to the emerging theory of data analysis, the as yet largely atheoretical and informal process that precedes and supports formal statistical activities.

Suggested Citation

  • David Draper & James S. Hodges & Colin L. Mallows & Daryl Pregibon, 1993. "Exchangeability and Data Analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 156(1), pages 9-28, January.
  • Handle: RePEc:bla:jorssa:v:156:y:1993:i:1:p:9-28
    DOI: 10.2307/2982858
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    Cited by:

    1. Jonathan L. Blitstein & Peter J. Hannan & David M. Murray & William R. Shadish, 2005. "Increasing the Degrees of Freedom in Existing Group Randomized Trials," Evaluation Review, , vol. 29(3), pages 241-267, June.
    2. Borsato, Luísa & Horta, Eduardo & Souza, Rafael Rigão, 2024. "Product disintegrations: A law of large numbers via conditional independence," Statistics & Probability Letters, Elsevier, vol. 208(C).
    3. Steven N. Durlauf, 2002. "On the Empirics of Social Capital," Economic Journal, Royal Economic Society, vol. 112(483), pages 459-479, November.
    4. Uwe Saint-Mont, 2015. "Randomization Does Not Help Much, Comparability Does," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-24, July.
    5. Luger, Richard, 2006. "Exact permutation tests for non-nested non-linear regression models," Journal of Econometrics, Elsevier, vol. 133(2), pages 513-529, August.
    6. Sander Greenland, 2001. "Putting Background Information About Relative Risks into Conjugate Prior Distributions," Biometrics, The International Biometric Society, vol. 57(3), pages 663-670, September.
    7. Brock,W.A. & Durlauf,S.N., 2000. "Growth economics and reality," Working papers 24, Wisconsin Madison - Social Systems.
    8. Yuli Liang & Dietrich Rosen & Tatjana Rosen, 2021. "On properties of Toeplitz-type covariance matrices in models with nested random effects," Statistical Papers, Springer, vol. 62(6), pages 2509-2528, December.
    9. Courgeau, Daniel, 2012. "Probability and social science : methodologial relationships between the two approaches ?," MPRA Paper 43102, University Library of Munich, Germany.

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