Approximate Bayesianity of Frequentist Confidence Intervals for a Binomial Proportion |
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Authors: | Shaobo Jin Måns Thulin Rolf Larsson |
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Affiliation: | 1. Department of Statistics, Uppsala University, Uppsala, Sweden;2. Department of Mathematics, Uppsala University, Uppsala, Sweden |
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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. |
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Keywords: | Asymptotic expansion Binomial distribution Credible interval |
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