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Calibrated Bayesian credible intervals for binomial proportions. (English) Zbl 07194274
Summary: Drawbacks of traditional approximate and exact confidence intervals for binomial proportions are well recognized. Alternatives include an interval based on inverting the score test, adaptations of exact testing, and Bayesian credible intervals. We propose an approach that calls for selecting an optimal value $$\kappa$$ between 0 and 0.5 based on stipulated coverage criteria over a grid of regions comprising the parameter space. One then bases lower and upper limits of a credible interval on Beta $$( \kappa, 1- \kappa)$$ and Beta $$(1- \kappa, \kappa)$$ priors, respectively. The result tends toward a Jeffreys prior-based interval if the goal is to constrain average overall coverage at $$\leq 1- \alpha$$ across the full parameter space, and toward the Clopper-Pearson interval if the goal is to constrain region-specific lower and upper lack of coverage rates $$\leq \alpha /2$$ as region widths approach zero. We suggest an intermediate target that demonstrably improves region-specific coverage balance when compared with existing methods.
MSC:
 62 Statistics
SAS; SAS/STAT
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