Custom Orthogonal Weight functions (COWs) for event classification
Custom Orthogonal Weight functions (COWs) for event classification
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DOI：
10.1016/j.nima.2022.167270
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
H. Dembinski;M. Kenzie;C. Langenbruch;M. Schmelling
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文献类型：
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作者：
H. Dembinski;M. Kenzie;C. Langenbruch;M. Schmelling
数据分析中的一个常见问题是信号和背景的分离。我们重新审视和概括所谓的Weightsmethod，它允许一个控制变量的信号密度的经验估计计算使用一个适合的混合信号和背景模型的判别变量。我们表明，权是一个特殊的情况下，更大的一类自定义正交权重函数（COWs），它可以应用到更一般的一类问题，其中的歧视和控制变量不一定是独立的，仍然达到接近最佳性能。我们还研究了从统计模型拟合加权数据估计的参数的性质，并提供了拟合参数的渐近协方差矩阵的封闭公式。为了说明我们的研究结果，我们讨论了这些技术的几个实际应用。
A common problem in data analysis is the separation of signal and background. We revisit and generalise the so-calledsWeightsmethod, which allows one to calculate an empirical estimate of the signal density of a control variable using a fit of a mixed signal and background model to a discriminating variable. We show thatsWeightsare a special case of a larger class of Custom Orthogonal Weight functions (COWs), which can be applied to a more general class of problems in which the discriminating and control variables are not necessarily independent and still achieve close to optimal performance. We also investigate the properties of parameters estimated from fits of statistical models tosWeighteddata and provide closed formulas for the asymptotic covariance matrix of the fitted parameters. To illustrate our findings, we discuss several practical applications of these techniques.