arXiv subjects

Jordan Tucker

Publications and source records attributed to Jordan Tucker.

2 recordsLinked to original sources

arXiv2009

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.

physics.data-an↗

arXiv2008

Evaluation of three methods for calculating statistical significance when incorporating a systematic uncertainty into a test of the background-only hypothesis for a Poisson process

Hypothesis tests for the presence of new sources of Poisson counts amidst background processes are frequently performed in high energy physics (HEP), gamma ray astronomy (GRA), and other branches of science. While there are conceptual issues already when the mean rate of background is precisely known, the issues are even more difficult when the mean background rate has non-negligible uncertainty. After describing a variety of methods to be found in the HEP and GRA literature, we consider in detail three classes of algorithms and evaluate them over a wide range of parameter space, by the criterion of how close the ensemble-average Type I error rate (rejection of the background-only hypothesis when it is true) compares with the nominal significance level given by the algorithm. We recommend wider use of an algorithm firmly grounded in frequentist tests of the ratio of Poisson means, although for very low counts the over-coverage can be severe due to the effect of discreteness. We extend the studies of Cranmer, who found that a popular Bayesian-frequentist hybrid can undercover severely when taken to high Z values. We also examine the profile likelihood method, which has long been used in GRA and HEP; it provides an excellent approximation in much of the parameter space, as previously studied by Rolke and collaborators.

physics.data-an↗