Approximate Bayesianity of Frequentist Confidence Intervals for a Binomial Proportion

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 . . 0.317, the Bayesian interval based on the Jeffreys. prior is then shown to be a compromise between the likelihood ratio and Wilson intervals.