Approximate Bayesianity of Frequentist Confidence Intervals for a Binomial Proportion

Shaobo Jin, Måns Thulin and Rolf Larsson

The American Statistician, 2017, vol. 71, issue 2, 106-111

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.

Date: 2017
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DOI: 10.1080/00031305.2016.1208630

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