PHYSTAT informal review:sPlots

by Chad Shafer (CMU), Michael Schmelling (Max Planck Society (DE))

Wednesday 21 May 2025, 15:30 → 17:00 Europe/Zurich

This is a PHYSTAT Informal Review event*. Today Michael Schmelling (physicist) together with Chad Shafer (statistician) will review the topic "sPlots".  For an intro into the topic see this talk

Agenda:

• 3.30 pm Opening:
• 3.30 pm Physicists Presentation (20'+10')
• 4 pm Statisticians Presentation (20'+10')
• 4.30 pm General Discussion and Closing (30')

 

Abstract: 

A common problem in particle physics is that a signal studied as a function of a ``control variable'' y is contaminated by background. Even if signal and background are indistinguishable at the level of single measurements, background can be removed if it statistically separates in a ``discriminant variable'' x. The sPlot method assumes that the joint PDF of signal and background is a density mixture, where both signal and background factorize in x and y, and where the PDFs in x are known. Extraction of the signal in y then is possible by histogramming the data in y with weights w(x), where w(x) is a function that is orthogonal to the background density in x.

There is considerable freedom to construct such Custom Orthogonal Weight functions (COWs). A special case are sWeights, which minimize the total variance of the histogram in y. Focussing on their mathematical properties, COWs are derived as a way to perform unbinned fits in a single variable x. Their use in the sPlot method to disentangle signal and background in y then comes as a natural extension, which generalizes the classical sWeights/sPlot method to shape parameters in the PDFs of the discriminant variable x.

Moving on, the second part will describe connections between the COWs approach and existing statistical models, and explore how these connections can lead to extensions, and help address some interesting questions including the potential to assess goodness-of-fit, the identifiability of related models, and the challenges of uncertainty quantification.

 

*PHYSTAT informal reviews: In this virtual format, a Tandem consisting of a physicist and a statistician will review a statistical method introduced by one of the parties or a general critical analysis topic from the Physicist's and Statistician's perspectives. The virtual events comprise: two 20+10 min. complementary presentations followed by ~30 minutes of general discussion.

 

Chad_Schafer.pdf

GMT20250521-133215_Recording_1976x1112.mp4

Michael_Schmelling.pdf