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A fair comparison of credible and confidence intervals: an example with binomial proportions

Author

Listed:
  • Tuany Paula Castro

    (Universidade de São Paulo)

  • Carlos Daniel Paulino

    (IST and CEAUL, FCUL, Universidade de Lisboa)

  • Julio M. Singer

    (Universidade de São Paulo)

Abstract

Comparison between confidence and credible intervals is complicated in view of their different nature: confidence intervals are random and credible intervals are numeric. A fair comparison should take this difference into account. Motivated by the similarity of a confidence interval proposed by Agresti and Coull (Am Stat 52:119–126, 1998) and a Bayesian credible interval based on a Beta(2,2) prior distribution for a Binomial proportion, we design algorithms where the comparison is conducted under the same paradigm, i.e., considering the Bayesian intervals (central and HPD) as realizations of random intervals and treating confidence intervals as numeric. In our example, intervals are compared via simulation studies that show a better performance of the Wilson (score) and HPD uniform prior intervals with some advantages of Bayesian intervals with respect to the expected and posterior length.

Suggested Citation

  • Tuany Paula Castro & Carlos Daniel Paulino & Julio M. Singer, 2022. "A fair comparison of credible and confidence intervals: an example with binomial proportions," METRON, Springer;Sapienza Università di Roma, vol. 80(3), pages 371-382, December.
    • Handle: RePEc:spr:metron:v:80:y:2022:i:3:d:10.1007_s40300-021-00225-6
    DOI: 10.1007/s40300-021-00225-6
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    References listed on IDEAS

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    1. Alan Agresti & Yongyi Min, 2005. "Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables," Biometrics, The International Biometric Society, vol. 61(2), pages 515-523, June.
    2. Shaobo Jin & Måns Thulin & Rolf Larsson, 2017. "Approximate Bayesianity of Frequentist Confidence Intervals for a Binomial Proportion," The American Statistician, Taylor & Francis Journals, vol. 71(2), pages 106-111, April.
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