Proposed method for counting experiment combinations: Likelihood-Ratio (LR)

• Short introduction to the method:

The likelihood-Ratio method has been adopted at LEP to combine searches results in terms of signal exclusions and comparison with background only hypothesis. This method, based on a frequentist approach, gives a clear prescription on how to compute Confidence Levels related to the outcome of a search. The Confidence Levels relative to data outcome (or expected data outcomes) can be computed assuming different hypothesis on the underlying physics process that is responsible for the experimental observation (typically background only hypothesis and signal plus background hypothesis).
The statistical variable that is chosen to compute the CL is the ratio of the likelihood for the two hypothesis
• LR=L(s+b)/L(b)
This Likelihood is a function of the outcome of the experiments (i.e. it is a statistical observable) and of external parameters like the expectations of number of signal and background events. This statistical variable has a nice ordering properties: it tends to be larger if the data are in distributed on the basis of signal plus background hypothesis instead of being distributed on the basis of background only hypothesis.
• General information on Confidence Level calculation can be found at the Workshop on confidence limits held at CERN in year 2000. There you can find also some more detailed bibliography on LR technique.
• Some introductory transparencies on Confidence Levels based on Likelihood-Ratio method (talks given during Higgs wg meeting) can be found at:
• F.Cerutti: Higgs wg presentation
• K.Cranmer Higgs wg presentation
• E.Gross: hep-ex/0211058

Single channel significance

• Simple programs to compute expected significance on single channel counting experiments based on Poisson statistics (it includes the possibility to add systematics on signal and bkg with simple rescaling method):
• /afs/cern.ch/user/f/fcerutti/public/clb_pub.exe
• Similar program from Wisconsin web page
• PoissonSig and PoissonSig_syst (systematics on bkg included)


Multichannels counting experiments combination

• Simple program based on LR (it includes crude systematics based on signal reduction and background increase by their systematics uncertainties); it combines up to 10 statistical independent channels. It is not very suitable for experiments with large number of background events (larger than ~500):
• /afs/cern.ch/user/f/fcerutti/public/lrfft_pub.exe

Multichannels counting experiments and discriminating variables combination

• Combination program can be downloaded from Wisconsin web page
• Likelihood and Likelihood_syst (with systematics error matrix)

Other LR-based codes from LEP

•  A Fast Probability Sum for the Likelihood Ratio Method of Combining Search Limits (web page maintained by T.Junk): http://thomasj.home.cern.ch/thomasj/searchlimits/ecl.html

Tools for selection optimization:
•  Projection and Correlation method  (Dean Karlen):here (thanks to Pauline Gagnon)

last update : F.Cerutti 3 April 2003