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.
翻译：高能物理学中一个反复出现的挑战是从观测数据分布中推断信号成分，这些观测数据通常被假设为信号事件与背景事件的混合。一个标准假设是，存在一个判别变量编码的信息能有效区分信号与背景。该信息可用于为每个事件分配信号权重，这些权重随后可用于对一个或多个感兴趣的控制变量进行分析。Dembinski等人（2022）提出的定制正交权重（COWs）方法，作为Barlow（1987）以及Pivk和Le Diberder（2005）提出的sPlot方法的推广，正是为实现这一目标而设计的。该问题及其解决方法呈现出新颖且引人关注的统计学议题。本文系统阐述了所需假设条件与统计特性，同时探讨了方法扩展及替代性方案。
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