.. _significance:


***************
Significance
***************
Significance estimations


ProfileLikelihood Calculator (roostats)

nominal case / no systematics:

using the entire mass range 7-14

x2 = 0.213796 +/- 0.0881078
x23 = 0.148275 +/- 0.0576889

the significance of this is 6.3 sigma


modified case i: restrict fit range

truncating the range to 8-14

x2 = 0.185549 +/- 0.0896092
x23 = 0.126762 +/- 0.064579

the significance goes down to 5.4 sigma

modified case ii: discard events

performing the nominal fit to a sub-set of the data (to inflate stat
errors) 

*********************************
Toy-based p-value estimtation
*********************************

plan: generate about 10**6 pseudo-experiments with either no systematics or latest evaluations (15\% for X23 and 10% for X2)


***********************
Profile likelihood ratio
***********************

Force x2 = 1, x3 = 1

.. image:: pyplots/ForceNoSuppreshiFitPt4.0.png
  :width: 300


.. image:: pyplots/ForceNoSuppresppFitPt4.0.png
  :width: 300

.. _importance_sampling:

Importance Sampling
-----------------

 RooFitResult: minimized FCN value: -79598.1, estimated distance to minimum: 0.000187477
                    covariance matrix quality: Full, accurate covariance matrix

        Constant Parameter    Value    
      --------------------  ------------
                 mscale_hi    1.0000e+00
                 mscale_pp    1.0000e+00
                      npow    2.3000e+00
                        x2    1.0000e+00
                        x3    1.0000e+00

        Floating Parameter  InitialValue    FinalValue +/-  Error     GblCorr.
      --------------------  ------------  --------------------------  --------
                     alpha    1.1178e+00    1.0872e+00 +/-  1.16e-01  <none>
                 bkg_a1_pp    3.6390e-01    2.9483e-01 +/-  8.27e-02  <none>
                 bkg_a2_pp   -4.3799e-01   -5.8112e-01 +/-  9.17e-02  <none>
                  decay_hi    6.0756e+00    6.5805e+00 +/-  7.83e-01  <none>
                        f2    1.1883e-01    1.6712e-01 +/-  2.62e-02  <none>
                        f3    2.4369e-02    7.1444e-02 +/-  2.42e-02  <none>
                   mean_hi    9.4552e+00    9.4555e+00 +/-  4.18e-03  <none>
                   mean_pp    9.4457e+00    9.4512e+00 +/-  1.12e-02  <none>
                   nbkg_hi    1.1670e+04    1.1546e+04 +/-  1.44e+02  <none>
                   nbkg_pp    3.3735e+02    3.8035e+02 +/-  2.32e+01  <none>
                  nsig1_hi    1.3177e+03    1.3158e+03 +/-  7.35e+01  <none>
                  nsig1_pp    8.8229e+01    1.0544e+02 +/-  1.29e+01  <none>
                    sigma1    7.9382e-02    7.9284e-02 +/-  4.38e-03  <none>
                 turnOn_hi    7.8960e+00    7.7720e+00 +/-  1.89e-01  <none>
                  width_hi    2.2974e+00    2.2925e+00 +/-  2.56e-01  <none>

    chi2/ndf = (74.997 + 71.282)/125 = 1.170
    chi2 prob = 0.0938
    min nll = -79598.11763910



    the delta of S is         : 20.1263
    the delta of ndof is      : 2
    the C.L. is               : 1
    the significance level is : 6.01342 (one side)
    

    the C.L. is : 1,  the significance level is : 6.01342 sigma (one side)


*******************************************************************************
evaluate significance for systematic variations back of the envelope checks
*******************************************************************************

    based on nominal fit results

    from individual fits:

    PbPb

    N_{2S+3S}/N_{1S}    0.155 +/-  0.038
     N_{2S}/N_{1S}          0.127 +/-  0.027

    pp
     N_{2S+3S}/N_{1S}    0.879 +/-  0.17
     N_{2S}/N_{1S}          0.496 +/-  0.12
           
    pp-PbPb
     N_{2S+3S}/N_{1S}    0.724 +/-  0.17
     N_{2S}/N_{1S}          0.369 +/-  0.12

    pp-PbPb: #sigmas away from zero [note this assumes gaussian errors]
    0.72/0.17 = 4.3
    0.37/0.12 = 3.1

    maximum significance allowed by pp data alone (assume full suppression in PbPb):
     0.879/0.17=5.2
     0.496/0.12=4.1


    from simultaneous fit:

    x23 = 0.147 +/- 0.048

    x2   = 0.214 +/- 0.069

    x3   = 0.059 +/- 0.060

    #sigmas away from unit [note however ratio of gaussian pdf's is not gaussian!]

    (1 - 0.147) / 0.048 ~ 18  

    (1 - 0.214) / 0.069 ~14    

.. _importance_sampling:

Importance Sampling
-----------------

 .. plot:: pyplots/xsection.py
     :include-source:

.. image:: pyplots/UPC_pt_graphlog.png
 

:ref:`custom_look`.