Coverage-adjusted confidence intervals for a binomial proportion

TL;DR

This paper introduces coverage-adjusted confidence intervals for binomial proportions that improve coverage accuracy and are shorter, especially for p near 0 or 1, by leveraging prior and posterior distributions.

Contribution

It proposes a novel coverage-adjustment method for Clopper-Pearson intervals using Bayesian priors and posteriors, enhancing their performance.

Findings

Coverage-adjusted intervals have better coverage accuracy.

Adjusted intervals are often shorter than existing methods.

Intervals are especially effective when p is close to 0 or 1.

Abstract

We consider the classic problem of interval estimation of a proportion $p$ based on binomial sampling. The "exact" Clopper-Pearson confidence interval for $p$ is known to be unnecessarily conservative. We propose coverage-adjustments of the Clopper-Pearson interval using prior and posterior distributions of $p$. The adjusted intervals have improved coverage and are often shorter than competing intervals found in the literature. Using new heatmap-type plots for comparing confidence intervals, we find that the coverage-adjusted intervals are particularly suitable for $p$ close to 0 or 1.