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Approximate Bayesianity of frequentist confidence intervals for a binomial proportion
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0003-0336-2974
2017 (English)In: American Statistician, ISSN 0003-1305, E-ISSN 1537-2731, Vol. 71, 106-111 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2017. Vol. 71, 106-111 p.
Keyword [en]
Asymptotic expansion; Binomial distribution; Credible interval
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-330868DOI: 10.1080/00031305.2016.1208630ISI: 000405647200002OAI: oai:DiVA.org:uu-330868DiVA: diva2:1147267
Available from: 2017-10-05 Created: 2017-10-05 Last updated: 2017-10-24Bibliographically approved

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Publisher's full texthttp://www.tandfonline.com/doi/full/10.1080/00031305.2016.1208630

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Jin, ShaoboEriksson, MånsLarsson, Rolf

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