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Expressing Regret: A Unified View of Credible Intervals

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  • Kenneth Rice
  • Lingbo Ye

Abstract

Posterior uncertainty is typically summarized as a credible interval, an interval in the parameter space that contains a fixed proportion—usually 95%—of the posterior’s support. For multivariate parameters, credible sets perform the same role. There are of course many potential 95% intervals from which to choose, yet even standard choices are rarely justified in any formal way. In this article we give a general method, focusing on the loss function that motivates an estimate—the Bayes rule—around which we construct a credible set. The set contains all points which, as estimates, would have minimally-worse expected loss than the Bayes rule: we call this excess expected loss “regret.” The approach can be used for any model and prior, and we show how it justifies all widely used choices of credible interval/set. Further examples show how it provides insights into more complex estimation problems. Supplementary materials for this article are available online.

Suggested Citation

  • Kenneth Rice & Lingbo Ye, 2022. "Expressing Regret: A Unified View of Credible Intervals," The American Statistician, Taylor & Francis Journals, vol. 76(3), pages 248-256, July.
  • Handle: RePEc:taf:amstat:v:76:y:2022:i:3:p:248-256
    DOI: 10.1080/00031305.2022.2039764
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    Cited by:

    1. Eleni Verykouki & Christos T. Nakas, 2023. "Adaptations on the Use of p -Values for Statistical Inference: An Interpretation of Messages from Recent Public Discussions," Stats, MDPI, vol. 6(2), pages 1-13, April.

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