Calibrated Bayesian Credible Intervals for Binomial Proportions
Drawbacks of traditional approximate (Wald test-based) and exact (Clopper-Pearson) confidence intervals for a binomial proportion are well-recognized. Alternatives include an interval based on inverting the score test, adaptations of exact testing, and Bayesian credible intervals derived from unifor...
| Veröffentlicht in: | Journal of statistical computation and simulation. - 1999. - 90(2020), 1 vom: 28., Seite 75-89 |
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| Weitere Verfasser: | , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2020
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| Zugriff auf das übergeordnete Werk: | Journal of statistical computation and simulation |
| Schlagworte: | Journal Article Approximate inference Confidence interval Exact inference Lower bound Upper bound |
| Zusammenfassung: | Drawbacks of traditional approximate (Wald test-based) and exact (Clopper-Pearson) confidence intervals for a binomial proportion are well-recognized. Alternatives include an interval based on inverting the score test, adaptations of exact testing, and Bayesian credible intervals derived from uniform or Jeffreys beta priors. We recommend a new interval intermediate between the Clopper-Pearson and Jeffreys in terms of both width and coverage. Our strategy selects a value κ between 0 and 0.5 based on stipulated coverage criteria over a grid of regions comprising the parameter space, and bases lower and upper limits of a credible interval on Beta(κ, 1- κ) and Beta(1- κ, κ) priors, respectively. The result tends toward the Jeffreys interval if the criterion is to ensure an average overall coverage rate (1-α) across a single region of width 1, and toward the Clopper-Pearson if the goal is to constrain both lower and upper lack of coverage rates at α/2 with region widths approaching zero. We suggest an intermediate target that ensures all average lower and upper lack of coverage rates over a specified set of regions are ≤ α/2. Interval width subject to these criteria is readily optimized computationally, and we demonstrate particular benefits in terms of coverage balance |
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| Beschreibung: | Date Revised 01.01.2021 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 0094-9655 |
| DOI: | 10.1080/00949655.2019.1672695 |