sPlot: a statistical tool to unfold data distributions

sPlot: a statistical tool to unfold data distributions

2 Sep 2005 | M. Pivk and F.R. Le Diberder
This paper introduces a statistical tool called $ _{s} $ Plot to explore data samples composed of multiple event sources. The $ _{s} $ Plot technique allows the reconstruction of the contributions of different sources to the distribution of a data sample in a given variable, without prior knowledge of that variable. It is applied within the context of a Likelihood fit, which determines the yields of the various sources. The technique is based on the assumption that the control variable is uncorrelated with the discriminating variable. The $ _{s} $ Plot formalism is developed to reconstruct the distributions of control variables for each source of events, using the knowledge of the discriminating variables. The technique is implemented through a covariance-weighted weight, which allows for the accurate reconstruction of the true distributions. The $ _{s} $ Plot technique is validated through examples and applications, including the reconstruction of control variable distributions and the correction of yields for selection efficiencies. The technique is shown to be effective in separating signal and background events and to provide accurate statistical uncertainties. The $ _{s} $ Plot method is implemented in the ROOT framework and has been applied to various data samples, demonstrating its effectiveness in reconstructing distributions and extracting physics results.This paper introduces a statistical tool called $ _{s} $ Plot to explore data samples composed of multiple event sources. The $ _{s} $ Plot technique allows the reconstruction of the contributions of different sources to the distribution of a data sample in a given variable, without prior knowledge of that variable. It is applied within the context of a Likelihood fit, which determines the yields of the various sources. The technique is based on the assumption that the control variable is uncorrelated with the discriminating variable. The $ _{s} $ Plot formalism is developed to reconstruct the distributions of control variables for each source of events, using the knowledge of the discriminating variables. The technique is implemented through a covariance-weighted weight, which allows for the accurate reconstruction of the true distributions. The $ _{s} $ Plot technique is validated through examples and applications, including the reconstruction of control variable distributions and the correction of yields for selection efficiencies. The technique is shown to be effective in separating signal and background events and to provide accurate statistical uncertainties. The $ _{s} $ Plot method is implemented in the ROOT framework and has been applied to various data samples, demonstrating its effectiveness in reconstructing distributions and extracting physics results.
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