Higgs limit settings

Statistics Tools

RooStats

Using Tom Junk's mclimit_cms package

One Bin fitting

  • Xsig_clsTest.C - simple example to demonstrate usage of Tom's package
    • The results without nuisance parameters:
      Total signal this channel in this model: 118
      Total background this channel in this model: 327
      Input Data: 400
      >2 sigma probability: 0.9879
      >3 sigma probability: 0.9717
      >5 sigma probability: 0.7827
       test statistics of input data= -4.94491
       p-val = 0.0025 significance: 2.80703
            
    • This example plots the test statistics distribution of test hypothesis and null hypothesis
    • p-value is the probability of null hypothesis test statistics (red) less than observed test statistics (arrow). It means the probability of null hypothesis to be fluctuate to observed data. We can then convert p-value into one sided Gaussian width as significance.
    • blue histogram is the test statistics distribution of test hypothesis. We can use it to calculate the probability of observing N sigma excess, where N is defined from red histogram.
    • if the limit calculator reports p-value =0 for a given input data, It might indicate that we need more pseudo-experiments. The mclimit_csm.C requires at least one of the pseudo-experiments has test statistics less than that of the input data.
       
      Double_t mclimit_csm::omclbaux(Double_t tsaux)
      {
      
            if (tsb[itsb[i]] <= tsaux)
              {
                omclbloc = ((Double_t) i)/((Double_t) nmc);
              }
      }
            

Two Bin fitting

  • MultipleBins_clsTest.C - simple example to demonstrate usage of Tom's package
  • If we include another bin into fitting,
    • if the second bin has smaller statistics, it won't help improving the signal significance until the statistics uncertainty in the second bin compete with the systematics uncertainty.
    • if the second bin has large statistics, e.g. yield of 100. By assuming 100% correlated background of two bins, the second bin can constraint 10% level of the background in the first bin. Therefor, we can see sizeable improvement by including the second bin.

-- ShihChiehHsu - 04 Jul 2008

Topic attachments
I Attachment History Action Size Date Who Comment
C source code filec MultipleBins_clsTest.C r1 manage 9.3 K 2008-07-17 - 08:54 ShihChiehHsu test statistics by using two bins
C source code filec Xsig_clsTest.C r1 manage 5.1 K 2008-07-04 - 03:18 ShihChiehHsu simple example to demonstrate usage of Tom's package
GIFgif Xsig_clsTest_ZeroNuisance.gif r1 manage 14.4 K 2008-07-04 - 03:33 ShihChiehHsu Xsig_clsTest results of zero nuisance parameter
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Topic revision: r6 - 2011-12-13 - ShihChiehHsu
 
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