A fair comparison of credible and confidence intervals: an example with binomial proportions

Tuany Paula Castro (), Carlos Daniel Paulino () and Julio M. Singer ()
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Tuany Paula Castro: Universidade de São Paulo
Carlos Daniel Paulino: IST and CEAUL, FCUL, Universidade de Lisboa
Julio M. Singer: Universidade de São Paulo

METRON, 2022, vol. 80, issue 3, No 5, 382 pages

Abstract: Abstract Comparison between confidence and credible intervals is complicated in view of their different nature: confidence intervals are random and credible intervals are numeric. A fair comparison should take this difference into account. Motivated by the similarity of a confidence interval proposed by Agresti and Coull (Am Stat 52:119–126, 1998) and a Bayesian credible interval based on a Beta(2,2) prior distribution for a Binomial proportion, we design algorithms where the comparison is conducted under the same paradigm, i.e., considering the Bayesian intervals (central and HPD) as realizations of random intervals and treating confidence intervals as numeric. In our example, intervals are compared via simulation studies that show a better performance of the Wilson (score) and HPD uniform prior intervals with some advantages of Bayesian intervals with respect to the expected and posterior length.

Keywords: Binomial distribution; Coverage probability; Expected length; Highest posterior density (HPD) intervals (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s40300-021-00225-6

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