Particle physics experiments rely on the (generalised) likelihood ratio test (LRT) for searches and measurements, which consist of composite hypothesis tests. However, this test is not guaranteed to be optimal, as the Neyman-Pearson lemma pertains only to simple hypothesis tests. Any choice of test statistic thus implicitly determines how statistical power varies across the parameter space. An improvement in the core statistical testing methodology for general settings with composite tests would have widespread ramifications across experiments. We discuss an alternate test statistic that provides the data analyzer an ability to focus the power of the test on physics-motivated regions of the parameter space. We demonstrate the improvement from this technique compared to the LRT on a Higgs $\rightarrowττ$ dataset simulated by the ATLAS experiment and a dark matter dataset inspired by the LZ experiment. We also employ machine learning to efficiently perform the Neyman construction, which is essential to ensure statistically valid confidence intervals.

翻译：粒子物理实验依赖于（广义）似然比检验（LRT）进行搜索与测量，这些检验属于复合假设检验。然而，该检验方法并不保证最优性，因为奈曼-皮尔逊引理仅适用于简单假设检验。任何检验统计量的选择都会隐式决定统计功效在参数空间中的分布方式。针对复合检验的通用场景，核心统计检验方法的改进将对各类实验产生广泛影响。本文讨论一种替代检验统计量，使数据分析者能够将检验功效聚焦于参数空间中具有物理意义的区域。我们通过ATLAS实验模拟的希格斯玻色子→ττ衰变数据集及受LZ实验启发的暗物质数据集，展示了该方法相较于LRT的改进效果。同时，我们采用机器学习技术高效执行奈曼构造法，这对确保统计有效的置信区间至关重要。