-- AmnonHarel - 18-Sep-2010

Relevant hyperlinks

* Main page: AmnonHarelDijetCentralityRatio

Introduction

Following the meeting with the ARC on Septemer 14th, added the option of doing sideband fits during the ensemble testing. This allows us to study several new questions:
  1. are the fitted statistical uncertainties correct?
    • after all, this is a $\chi^2$ fit, which assumes each bin comes from a Gaussian ditribution
  2. what is the statistical significance (p-value) of the fitted shift?
  3. what are the consistency statistics and their p-values ifor models shifted to match data?

The fitted shift

NLO with non perturbative corrections
plot_shift.png plot_shift_a.png
plot_shift.root plot_shift_a.root
  • The distribution (with systematics, which widen it a bit) of the fitted statistical errors is close to a Gaussian( 0.0145, 0.0007 )
    • the value in data (0.0133) is well within this distribution.
    • but this shows that the fitted statistical uncertainties are significantly underestimated
  • Not too interesting to derive similar plots for Pythia - the ensembles distributions will be similar, but the relevant |shift| is only 0.011

Consistency statistic for fitted models

  • currently the code does not allow testing this for the procedure used in the limit setting, i.e., no overlap between the fitted region and the signal region.
    • that's fine - as this test is redundant, it's just an externally determined shift.
  • can test the QCD models with the fit done on the entire range
    • the systematics are a bit different than in the limit setting case - the full shape of the NPcorr and PDF uncertainties is used, rather than a flat offset appropriate to the normalization region. This is a new feature (20th September), and is important when testing the consistency statistic for shifted models, as the shift "takes away" the effect of the flat systematic variations.
    • the behavior of the shift is quite expected - smaller statistical uncertainties can not explain the observed value, but the systematics can
plot_qcd_shift.png
  • results for the consistency statistic are surprising - the consistency in the ensemble tests is bad (high C values), leading to a p-value of >95%.

Technicalities

  • needed to add a new fitting method, with a custom likelihood whose inputs are two histograms. The usual technique is to fit a function to a histogram, but the functions are not available during ensemble testing as some of the systematic variations are done on the binned histograms derived from the functions.
  • a few subtle changes needed throughout to accomodate this.
  • the two fitting methods agree to 1-2% relative (since we quote up to two significant figures, both agree on the quoted numbers)

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PNGpng plot_qcd_shift.png r2 r1 manage 25.8 K 2010-09-21 - 18:05 AmnonHarel  
Unknown file formatroot plot_qcd_shift.root r1 manage 19.4 K 2010-09-21 - 18:06 AmnonHarel  
PNGpng plot_shift.png r4 r3 r2 r1 manage 27.9 K 2010-09-18 - 23:35 AmnonHarel  
Unknown file formatroot plot_shift.root r1 manage 19.4 K 2010-09-18 - 23:36 AmnonHarel  
PNGpng plot_shift_a.png r4 r3 r2 r1 manage 17.5 K 2010-09-18 - 23:35 AmnonHarel  
Unknown file formatroot plot_shift_a.root r2 r1 manage 15.3 K 2010-09-18 - 23:36 AmnonHarel  
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Topic revision: r4 - 2010-09-21 - AmnonHarel
 
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