Calibrated Bayesian Credible Intervals for Binomial Proportions.
Abstract
(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.