PHYSTAT informal review: Errors on Errors

by Enzo Canonero (University of London (GB)), Glen Cowan (Royal Holloway, University of London), Richard Lockhart (SFU)

Wednesday 30 Oct 2024, 15:30 → 17:00 Europe/Zurich

This is a PHYSTAT Informal Review event*. Today Glen Cowan and Enzo Canonero (physicists, RHUL) together with Richard Lockhart (Statistician, SFU) will review the topic "Errors on Errors".

Agenda:

• 3.30 pm Opening: Olaf Behnke
• 3.30 pm Presentation Enzo Canonero & Glen Cowan (20'+10')
• 4 pm Presentation Richard Lockhart (20'+10')
• 4.30 pm General Discussion and Closing (30')

 

Your show master today is: Sara Algeri 

• If you have a questions/comment:
  • during a presentation: please write into the ZOOM chat box
  • after a presentation: write into chat box and/or raise hand and we will call you.
• Please obey the PHYSTAT Code of Conduct

 

Abstract: The session will begin with an introduction to the Gamma Variance Model (GVM), a statistical framework that incorporates uncertainties in the assignment of systematic errors, informally known as "errors-on-errors". This model is particularly useful in analyses that combine results from multiple measurements. Traditionally, such combinations have been performed using either the Best Linear Unbiased Estimator (BLUE) method or the nuisance-parameter method. In this talk, we useful relations that connect the BLUE and nuisance-parameter approaches when the correlations induced by systematic uncertainties are non-trivial (i.e., not simply $\pm 1$ or $0$) will be presented. Generalizations of the nuisance-parameter approach to include errors-on-errors will also be proposed. Furthermore, since statistical models that incorporate errors-on-errors deviate from first-order asymptotic behaviour, it will be demonstrated how "higher-order asymptotics" can be employed to derive analytical formulas for computing precise confidence intervals. Finally, applications of this framework to the $7$–$8$ TeV ATLAS-CMS top quark mass combination will be presented.

The second part of the session will applaud this gamma variance model effort,  argue that statistical analysis is full of optimistic estimates of uncertainty and that errors on errors is a very helpful response to that problem,  and to discuss issues which might or might not arise in special cases.  Consideration will be given to the scope of the frequentist paradigm,  the role of independence in the strategy, and the role of dimension in these problems. Connections will be drawn with work in meta-analysis and other related ideas with topic names like “Transporting Evidence” and “External Studies”. If time allows, estimating equations will also be covered.

*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.

 

Enzo_Canonero.pdf

GMT20241030-143316_Recording_1920x1124.mp4

Richard_Lockhart.pdf