Custom Orthogonal Weight functions (COWs) for Event Classification

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 discrimin...

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Bibliographic Details
Published in:arXiv.org 2022-01
Main Authors: Dembinski, Hans, Kenzie, Matthew, Langenbruch, Christoph, Schmelling, Michael
Format: Article
Language:English
Subjects:
Covariance matrix
Data analysis
Empirical analysis
Independent variables
Parameter estimation
Statistical models
Weighting functions
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2112.04574