Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frequentist Evaluation of Intervals Estimated for a Binomial Parameter
  and for the Ratio of Poisson Means   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. In most of the
statistics literature, this averaging is over different values of the unknown
parameter, which is conceptually problematic from the frequentist point of view
in which the unknown parameter is typically fixed. In contrast, we perform an
(unconditional) {\it average over observed data} in the ratio-of-Poisson-means
problem. If strict conditional coverage is desired, we recommend
Clopper-Pearson intervals and intervals from inverting the likelihood ratio
test (for central and non-central intervals, respectively). Lancaster's mid-$P$
modification to either provides excellent unconditional average coverage in the
ratio-of-Poisson-means problem.

0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th