Approximate Bayesianity of Frequentist Confidence Intervals for a Binomial Proportion

作者：Jin Shaobo^*; Thulin Mans; Larsson Rolf

来源：American Statistician, 2017, 71(2): 106-111.

DOI：10.1080/00031305.2016.1208630

• Asymptotic expansion
• Binomial distribution
• Credible interval

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 alpha less than or similar to 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.

• 出版日期2017-5