Frequentist Evaluation of Intervals Estimated for a Binomial Parameter and for the Ratio of Poisson Means

Understand

Confidence intervals for a binomial parameter or for the ratio of Poisson means are commonly desired in high energy physics (HEP) applications such as measuring a detection efficiency or branching ratio.

• Due to the discreteness of the data, in both of these problems the frequentist coverage probability unfortunately depends on the unknown parameter.
• Trade-offs among desiderata have led to numerous sets of intervals in the statistics literature, while in HEP one typically encounters only the classic intervals of Clopper-Pearson (central intervals with no undercoverage but substantial over-coverage) or a few approximate methods which perform rather poorly.
• If strict coverage is relaxed, some sort of averaging is needed to compare intervals.