This page documents the tutorial for the "LPC Stats II Hands On Tutorial Event", focusing on the usage of the CMS combination tool to extract the signal strength, statistical significance and upper limits in a physics model.

General Introduction

In this tutorial, we use the H->WW->lnln analysis as an example to illustrate how to build a physics analysis based on both cut-n-count and shape method and calculate the upper limits, significance. For simplification, we use ideal MC sample without reconstruction and include only one background (continuum WW) in the search.

Disclaimer: Numbers in this tutorial are motivated by the HWW analysis, but do not have one-to-one correspondance to the HWW results. Please do not be alarmed that your result is not the same as in the official note or AN.

Setting up the environment for executable combine

note: as for the rest of CMSSW software, this requires scientific linux 5, so you should log into lxplus5.cern.ch and not lxplus.cern.ch

 
setenv SCRAM_ARCH slc5_amd64_gcc472 # use export SCRAM_ARCH=slc5_amd64_gcc472 for bash
cmsrel  CMSSW_6_1_1
cd CMSSW_6_1_1/src 
cmsenv
addpkg HiggsAnalysis/CombinedLimit V03-01-12
scramv1 b

After this, you have an excutable called "combine" that can be used to do tons of statistical calculations. Use combine help to see the ultimate list of options.

Building cut-based analysis

In a cut and count analysis, we need to know what is the number of signal and background events expected, the number of events observed in data and associated systematic uncertainties. Each source of the systematic uncertainty is labelled as a nusiance. It is important to notice that even the MC statistic error for a given background is assumed as a nusiance.

Datacard

Datacard is the input to run the statistical tools in the Higgs analysis in CMS. This can be adapted for other search program as well. There are two different softwares in CMS that does this computation, one is in LandS and other is in HiggsLimit/combination. The common data card for a cut-based analysis is given below.

Here is an example of the card called hww_20fb_cut.txt. In this example we consider 20% systematic uncertainty for the signal and 10% for the background.

imax 1 number of channels
jmax * number of background
kmax * number of nuisance parameters
Observation 505
bin                                   1       1
process                              HWW     qqWW
process                               0        1
rate                               90.000  430.000
uncert_HWW    lnN                   1.200   1.000 
uncert_qqWW   lnN                   1.000   1.100 

• This card needs to be reformatted to run within the HiggsAnalysis/CombinedLimit, by the following command.

combineCards.py of0j=hww_20fb_cut.txt > hww_20fb_cut_comb.txt

Note that if you have other channel (such as hww_20fb_1j_cut.txt), this can also combine them together by append other channels such as

combineCards.py of0j=hww_20fb_cut.txt of1j=hww_20fb_1j_cut.txt > hww_20fb_cut_comb.txt

Upper limit on the signal strength

combine -d hww_20fb_cut_comb.txt -M Asymptotic

Output:
 -- Asymptotic -- 
Observed Limit: r < 1.8221
Expected  2.5%: r < 0.6019
Expected 16.0%: r < 0.8016
Expected 50.0%: r < 1.1289
Expected 84.0%: r < 1.6194
Expected 97.5%: r < 2.2782
 

This indicates that the 95% upperlimit observed is 1.8, while the median expected is 1.1 with 1sigma band [0.8, 1.6] and 2sigma band [0.6, 2.2]. This result tells us that we observed an excess in data at the level of 1-2 sigma.

Expected significance

combine -d hww_20fb_cut_comb.txt  -M ProfileLikelihood -v 1 --significance --expectSignal=1 -t -1 -m 125 -n Expected

Output:
 -- Profile Likelihood -- 
Significance: 1.80964
       (p-value = 0.035176)

Observed significance

combine -d hww_20fb_cut_comb.txt  -M ProfileLikelihood -v 1 --significance --expectSignal=1 -t -1 -m 125
Output:
 -- Profile Likelihood -- 
Significance: 1.52713
       (p-value = 0.063364)

Best fit signal strength with uncertainty

A maximum likelihood scan is performed to get the +/- 1 sigma error.

combine -d hww_20fb_cut_comb.txt   -M MaxLikelihoodFit
Output:
 --- MaxLikelihoodFit ---
Best fit r: 0.832828  -0.535222/+0.559076  (68% CL)
nll S+B -> -6.19048  nll B -> -5.02441

Building Shape analysis

Datacard

Upperlimit on signal strength

Expected significance

Observed significance

Best fit signal strength with uncertainty

Useful Links

• Above tutorial is a super slimmed version of the complete tool, see the documentation here, Documentation of the RooStats-based statistics tools CMS