Title: COWs and their Hybrids: A Statistical View of Custom Orthogonal Weights Show Chinese title

Title: COWs及其混合：自定义正交权重的统计观点

Abstract: A recurring challenge in high energy physics is inference of the signal component from a distribution for which observations are assumed to be a mixture of signal and background events. A standard assumption is that there exists information encoded in a discriminant variable that is effective at separating signal and background. This can be used to assign a signal weight to each event, with these weights used in subsequent analyses of one or more control variables of interest. The custom orthogonal weights (COWs) approach of Dembinski, et al.(2022), a generalization of the sPlot approach of Barlow (1987) and Pivk and Le Diberder (2005), is tailored to address this objective. The problem, and this method, present interesting and novel statistical issues. Here we formalize the assumptions needed and the statistical properties, while also considering extensions and alternative approaches. Show Chinese abstract

Abstract: 在高能物理中，一个常见的挑战是从假设为信号和背景事件混合的分布中推断信号成分。 一种标准假设是，在判别变量中存在有效区分信号和背景的信息。 这可以用来为每个事件分配一个信号权重，这些权重用于后续对一个或多个感兴趣控制变量的分析。 Dembinski 等人（2022）的自定义正交权重（COWs）方法，是对 Barlow（1987）和 Pivk 与 Le Diberder（2005）的 sPlot 方法的一种推广，专门用于解决此目标。 这个问题以及这种方法提出了有趣且新颖的统计问题。 在这里，我们明确所需的假设和统计特性，同时考虑扩展和替代方法。