> Confidence level computation guidelines for the Physics TDR
> Conclusion of CL meeting with the BSM/SUSY and Higgs convenors 11/10/05
> - The prime significance estimator choosen for the CMS PTDR is S_cL,
> because of its extendibility to shapes of distributions, not just event
> counting.
> For event counting however it was shown [Quast, Barschke] that the
> S_cP estimator gives essentially an identical results, hence this can
> be used as well.
> - The procedure to include systematic errors into event counting
> discovery significance is to convolute Nb (Number of background events)
> in the Poisson distribution with a Gaussian (or other, e.g.
> theoretical systematic errors are generally not Gaussian but perhaps
> flat) to take into account the experimental systematic error.
> Note that in the limit of large Nb this leads to the simple formula
> significance = S / sqrt( Nb + DNb2)
> with S signal and DNb the systematic uncertainty on Nb
> - A tool is available for CMS to calculates S_cl and S_cP significance
> estimators, see appendix for details.
> In case for the S_cP ones, it is possible to include
> systematic uncertainties through a convolution of Nb with
> with a Gaussian (or other types of distributions) to get the limit
> according to the description above.
> A tool to have achieve the same for the S_cL significance estimator
> is planned for.
> - For the PTDR we describe the S_cL method as the basic one and remark the
> agreement with the S_cP one for event counting, to justify some
> results calculated with this significance estimator that may remain in
> the PTDR
> - This does not close the debate on CL estimators but defines a common
> scheme for the PTDR. We have to follow up the developements further,
> started with a few meetings during CMS weeks, for our preparation
> of first data.
> Appendix
> program to calculate S_cP significance taking into account background
> uncertainty can be found on
> http://cmsdoc.cern.ch/~bityukov/
> "Program for calculations of the significance S_cP"
> "fast version without MC and with smoothing in the case non-integer
> amus+amub"
> it is a fortran program; simple script to run it is also on the page:
> "Macros for the fast version of program (./scpf.job)"
> the input must be put inside the program :
> 1. number of signal events
> 2. number of background events
> 3. uncertainty of number the background events squared
> S_cP calculates probability (in number of sigmas) that background with
> expected value NB fluctuates above observed number of events NB+NS with
> Poisson statistics. The uncertainty of the background DNB is taken into
> account as convolution of the Poisson with the background PDF. The
> Gaussian PDF of the background uncertainty is currently implemented.
> Others PDFs can be implemented as well.
> (A. De Roeck, P. Janot, S. Nikitenko, L. Pape, M. Spiropulu)

-- MariaSpiropulu - 18 Oct 2005

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