Coverage-adjusted Confidence Intervals for a Binomial Proportion

type="main" xml:id="sjos12021-abs-0001"> <title type="main">ABSTRACT</title>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 that incorporate prior or posterior beliefs into the interval. Using heatmap-type plots for comparing confidence intervals, we show that the coverage-adjusted intervals have satisfying coverage and shorter expected lengths than competing intervals found in the literature.