发表机构
Faculty of Physics, Moscow State University; Institute for Nuclear Research of the Russian Academy of Sciences; Branch of Lomonosov Moscow State University in Sarov（莫斯科国立大学物理系; 俄罗斯科学院核研究所; 莫斯科国立大学萨罗夫分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过蒙特卡洛模拟比较贝叶斯与Li-Ma准则，发现杰弗里斯先验的贝叶斯方法在On/Off分析中错误率更低且更稳健。
AI 中文摘要
我们详细比较了贝叶斯准则与三种无信息先验——平坦先验、杰弗里斯先验和尺度不变先验——在未知背景下检验信号的效果，并将其与经典频率学派的Li-Ma方法在On/Off问题中进行对比。我们针对不同背景水平进行了蒙特卡洛模拟，并通过第一类错误率评估了Li-Ma准则和贝叶斯准则。随后，我们模拟了非零信号，并根据第二类错误率比较了这些准则。我们发现，采用杰弗里斯先验的贝叶斯准则在两类错误率上均低于Li-Ma准则。此外，我们表明，当背景分布相对于泊松分布过度离散时，贝叶斯准则比Li-Ma准则更为稳健。
英文摘要
We present a detailed comparison of Bayesian criteria with three non-informative priors - flat, Jeffreys, and scale-invariant - for testing a signal against an unknown background and compare them with the classical frequentist Li-Ma approach in the On/Off problem. We perform Monte Carlo simulations for various background levels and evaluate the Li-Ma and Bayesian criteria by their Type I error rates. We then simulate a nonzero signal and compare the criteria in terms of Type II error rates. We find that both the Li-Ma criterion and the Bayesian criterion with the Jeffreys prior control Type I error well, excluding the case of small background $b < 0.5$; the Bayesian criterion with the Jeffreys prior is statistically more powerful than the Li-Ma criterion for $b \lesssim 40$.
Comments6 pages, 3 figures; v2: mistakes corrected
