当将系统不确定度纳入泊松过程的背景假设检验时，计算统计显著性的三种方法的评价
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
摘要：
背景过程中存在新的泊松计数源的假设检验经常在高能物理（HEP），伽马射线天文学（GRA）和其他科学分支中进行。虽然当背景的平均速率精确已知时已经存在概念问题，但是当平均背景速率具有不可忽略的不确定性时，这些问题甚至更加困难。在描述了各种方法被发现在HEP和GRA文献中，我们详细考虑三类算法，并评估它们在很宽的参数空间范围内，由标准的集合平均I型错误率（拒绝的背景只有假设时，它是真的）比较接近的标称显着性水平的算法。我们建议更广泛地使用一种算法，牢牢地扎根在频率主义测试的泊松比的手段，虽然非常低的计数的过度覆盖可能是严重的，由于离散的影响。我们扩展了克兰默的研究，他发现，一个流行的贝叶斯频率混合可以卧底严重时，采取高Z值。我们还研究了配置文件的似然方法，这已被长期用于GRA和HEP，它提供了一个很好的近似在大部分的参数空间，如以前研究的Rolke和合作者。
英文摘要：
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.
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