rf204_extrangefit.C File Reference

Detailed Description

'ADDITION AND CONVOLUTION' RooFit tutorial macro #204

Extended maximum likelihood fit with alternate range definition for observed number of events. If multiple ranges are used, or only a part of the data is fitted, it is advisable to use a RooAddPdf to extend the model. See tutorial 204a.

 
 
␛[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby␛[0m 
                Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
                All rights reserved, please read http://roofit.sourceforge.net/license.txt
 
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'signalRange' created with bounds [4,6]
[#1] INFO:Minization -- p.d.f. provides expected number of events, including extended term in likelihood.
[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization --  The following expressions have been identified as constant and will be precalculated and cached: (sig1,sig2)
[#1] INFO:Minization --  The following expressions will be evaluated in cache-and-track mode: (bkg)
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 a0           5.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
     2 a1           2.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
     3 nbkg         5.00000e+02  2.50000e+02    0.00000e+00  1.00000e+04
     4 nsig         5.00000e+02  2.50000e+02    0.00000e+00  1.00000e+04
     5 sig1frac     8.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
 **********
 **    3 **SET ERR         0.5
 **********
 **********
 **    4 **SET PRINT           1
 **********
 **********
 **    5 **SET STR           1
 **********
 NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
 **********
 **    6 **MIGRAD        2500           1
 **********
 FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
 START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
 FCN=-3945.08 FROM MIGRAD    STATUS=INITIATE       14 CALLS          15 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  a0           5.00000e-01   1.00000e-01   2.01358e-01   5.55992e+00
   2  a1           2.00000e-01   1.00000e-01   2.57889e-01  -1.57427e+00
   3  nbkg         5.00000e+02   2.50000e+02   1.18625e-01   2.53685e+00
   4  nsig         5.00000e+02   2.50000e+02   1.18625e-01  -2.53775e+00
   5  sig1frac     8.00000e-01   1.00000e-01   2.57889e-01  -2.02142e+00
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=-3945.49 FROM MIGRAD    STATUS=CONVERGED      98 CALLS          99 TOTAL
                     EDM=1.34919e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  a0           4.41701e-01   7.31971e-02   6.37371e-03  -2.20459e-02
   2  a1           2.01081e-01   1.18245e-01   8.18002e-03   7.34208e-03
   3  nbkg         5.04206e+02   3.94549e+01   4.96630e-04   1.70657e-02
   4  nsig         4.95799e+02   3.93537e+01   4.96929e-04   6.32308e-03
   5  sig1frac     8.37341e-01   1.17266e-01   8.52165e-03  -5.56324e-04
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  5    ERR DEF=0.5
  5.397e-03  1.216e-03 -3.098e-01  3.099e-01 -1.021e-03 
  1.216e-03  1.441e-02 -3.254e+00  3.254e+00 -9.763e-03 
 -3.098e-01 -3.254e+00  1.557e+03 -1.053e+03  3.292e+00 
  3.099e-01  3.254e+00 -1.053e+03  1.549e+03 -3.293e+00 
 -1.021e-03 -9.763e-03  3.292e+00 -3.293e+00  1.424e-02 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3      4      5
        1  0.14135   1.000  0.138 -0.107  0.107 -0.116
        2  0.77063   0.138  1.000 -0.687  0.689 -0.682
        3  0.77292  -0.107 -0.687  1.000 -0.678  0.699
        4  0.77488   0.107  0.689 -0.678  1.000 -0.701
        5  0.78168  -0.116 -0.682  0.699 -0.701  1.000
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        2500
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=-3945.49 FROM HESSE     STATUS=OK             31 CALLS         130 TOTAL
                     EDM=1.34689e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  a0           4.41701e-01   7.31850e-02   1.27474e-03  -1.16864e-01
   2  a1           2.01081e-01   1.17613e-01   3.27201e-04  -6.40802e-01
   3  nbkg         5.04206e+02   3.93107e+01   9.93261e-05  -1.11784e+00
   4  nsig         4.95799e+02   3.92054e+01   1.98772e-05  -1.12170e+00
   5  sig1frac     8.37341e-01   1.16841e-01   3.40866e-04   7.40533e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  5    ERR DEF=0.5
  5.395e-03  1.200e-03 -3.051e-01  3.051e-01 -1.005e-03 
  1.200e-03  1.425e-02 -3.209e+00  3.209e+00 -9.625e-03 
 -3.051e-01 -3.209e+00  1.545e+03 -1.041e+03  3.258e+00 
  3.051e-01  3.209e+00 -1.041e+03  1.537e+03 -3.258e+00 
 -1.005e-03 -9.625e-03  3.258e+00 -3.258e+00  1.413e-02 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3      4      5
        1  0.14023   1.000  0.137 -0.106  0.106 -0.115
        2  0.76770   0.137  1.000 -0.684  0.686 -0.678
        3  0.77101  -0.106 -0.684  1.000 -0.676  0.697
        4  0.77292   0.106  0.686 -0.676  1.000 -0.699
        5  0.77980  -0.115 -0.678  0.697 -0.699  1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization
 
  RooFitResult: minimized FCN value: -3945.49, estimated distance to minimum: 1.34689e-05
                covariance matrix quality: Full, accurate covariance matrix
                Status : MINIMIZE=0 HESSE=0 
 
    Floating Parameter    FinalValue +/-  Error   
  --------------------  --------------------------
                    a0    4.4170e-01 +/-  7.32e-02
                    a1    2.0108e-01 +/-  1.18e-01
                  nbkg    5.0421e+02 +/-  3.93e+01
                  nsig    4.9580e+02 +/-  3.92e+01
              sig1frac    8.3734e-01 +/-  1.17e-01
 

 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooAddPdf.h"
#include "RooExtendPdf.h"
#include "RooFitResult.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit;
 
void rf204_extrangefit()
{
 
   // S e t u p   c o m p o n e n t   p d f s
   // ---------------------------------------
 
   // Declare observable x
   RooRealVar x("x", "x", 0, 10);
 
   // Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
   RooRealVar mean("mean", "mean of gaussians", 5);
   RooRealVar sigma1("sigma1", "width of gaussians", 0.5);
   RooRealVar sigma2("sigma2", "width of gaussians", 1);
 
   RooGaussian sig1("sig1", "Signal component 1", x, mean, sigma1);
   RooGaussian sig2("sig2", "Signal component 2", x, mean, sigma2);
 
   // Build Chebychev polynomial p.d.f.
   RooRealVar a0("a0", "a0", 0.5, 0., 1.);
   RooRealVar a1("a1", "a1", 0.2, 0., 1.);
   RooChebychev bkg("bkg", "Background", x, RooArgSet(a0, a1));
 
   // Sum the signal components into a composite signal p.d.f.
   RooRealVar sig1frac("sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.);
   RooAddPdf sig("sig", "Signal", RooArgList(sig1, sig2), sig1frac);
 
   // C o n s t r u c t   e x t e n d e d   c o m p s   wi t h   r a n g e   s p e c
   // ------------------------------------------------------------------------------
 
   // Define signal range in which events counts are to be defined
   x.setRange("signalRange", 4, 6);
 
   // Associated nsig/nbkg as expected number of events with sig/bkg _in_the_range_ "signalRange"
   RooRealVar nsig("nsig", "number of signal events in signalRange", 500, 0., 10000) ;
   RooRealVar nbkg("nbkg", "number of background events in signalRange", 500, 0, 10000) ;
   
   // Use AddPdf to extend the model:
   RooAddPdf  model("model","(g1+g2)+a", RooArgList(bkg,sig), RooArgList(nbkg,nsig)) ;
   
   // Clone these models here because the interpretation of normalisation coefficients changes
   // when different ranges are used:
   RooAddPdf model2(model);
   RooAddPdf model3(model);
 
 
   // S a m p l e   d a t a ,   f i t   m o d e l
   // -------------------------------------------
 
   // Generate 1000 events from model so that nsig,nbkg come out to numbers <<500 in fit
   RooDataSet *data = model.generate(x, 1000);
 
   
   auto canv = new TCanvas("Canvas", "Canvas", 1500, 600);
   canv->Divide(3,1);
 
   // Fit full range
   // -------------------------------------------
 
   canv->cd(1);
 
   // Perform unbinned ML fit to data, full range
   RooFitResult* r = model.fitTo(*data,Save()) ;
   r->Print() ;
 
}

Author

07/2008 - Wouter Verkerke

Definition in file rf204_extrangefit.C.