A common problem in data analysis is the separation of signal and background. We revisit and generalise the so-called $sWeights$ method, 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 that $sWeights$ are 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 to $sWeights$ 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.
翻译:数据分析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“ $sWeights$” 方法,以便人们利用混合的信号和背景模型与区别变量相匹配,对控制变量的信号密度进行实证估计。 我们显示,$sWeights是较大类别的自定义正统重力函数(COWs)的特殊例子,可适用于更一般性的问题类别,在这些类别中,歧视和控制变量不一定独立,仍然接近于最佳性能。 我们还调查从统计模型的合适性参数到“$sWeights”的参数的属性,并为适合参数的无损共变矩阵提供封闭式公式。为了说明我们的调查结果,我们讨论了这些技术的几种实际应用。