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Approximate Bayesianity of Frequentist Confidence Intervals for a Binomial Proportion

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  • Shaobo Jin
  • Måns Thulin
  • Rolf Larsson

Abstract

The well-known Wilson and Agresti–Coull confidence intervals for a binomial proportion p are centered around a Bayesian estimator. Using this as a starting point, similarities between frequentist confidence intervals for proportions and Bayesian credible intervals based on low-informative priors are studied using asymptotic expansions. A Bayesian motivation for a large class of frequentist confidence intervals is provided. It is shown that the likelihood ratio interval for p approximates a Bayesian credible interval based on Kerman’s neutral noninformative conjugate prior up to O(n− 1) in the confidence bounds. For the significance level α ≲ 0.317, the Bayesian interval based on the Jeffreys’ prior is then shown to be a compromise between the likelihood ratio and Wilson intervals. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:amstat:v:71:y:2017:i:2:p:106-111
    DOI: 10.1080/00031305.2016.1208630
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    Cited by:

    1. 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.
    2. Xiang Liu & James Yang & Hui Soo Chae & Gary Natriello, 2020. "Power Divergence Family of Statistics for Person Parameters in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 502-525, June.

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