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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.

Coverage‐adjusted Confidence Intervals for a Binomial Proportion