sPlot: a statistical tool to unfold data distributions
Muriel Pivk, Francois R. Le Diberder
TL;DR
Addressing the challenge of separating contributions from multiple event sources in a single data sample, the paper introduces sPlot, a statistical tool to unfold the control-variable distributions of each source using only knowledge of the discriminating-variable PDFs. The method hinges on an extended Likelihood fit in the discriminating variables and constructs covariance-weighted weights (sWeights) that assign each event to a source for the control variable x. Key contributions include a complete formalism for sWeights, its normalization and uncertainty properties, and a practical implementation that allows merging sources and applying to branching-ratio studies. The approach enables unbiased, data-driven unfolding of per-source distributions in x, facilitating robust validation and interpretation of complex mixed-sample analyses.
Abstract
The paper advocates the use of a statistical tool dedicated to the exploration of data samples populated by several sources of events. This new technique, called sPlot, is able to unfold the contributions of the different sources to the distribution of a data sample in a given variable. The sPlot tool applies in the context of a Likelihood fit which is performed on the data sample to determine the yields of the various sources.