rf602_chi2fit.C File Reference

Detailed Description

Likelihood and minimization: setting up a chi^2 fit to a binned dataset

 
 
␛[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
 
[#0] WARNING:InputArguments -- The parameter 'sigma1' with range [-1e+30, 1e+30] of the RooGaussian 'sig1' exceeds the safe range of (0, inf). Advise to limit its range.
[#0] WARNING:InputArguments -- The parameter 'sigma2' with range [-1e+30, 1e+30] of the RooGaussian 'sig2' exceeds the safe range of (0, inf). Advise to limit its range.
[#0] WARNING:Eval -- Evaluating RooAddPdf without a defined normalization set. This can lead to ambiguos coefficients definition and incorrect results. Use RooAddPdf::fixCoefNormalization(nset) to provide a normalization set for defining uniquely RooAddPdf coefficients!
[#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 **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 bkgfrac      5.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
     4 sig1frac     8.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
 **********
 **    3 **SET ERR           1
 **********
 **********
 **    4 **SET PRINT           1
 **********
 **********
 **    5 **SET STR           1
 **********
 NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
 **********
 **    6 **MIGRAD        2000           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=106.175 FROM MIGRAD    STATUS=INITIATE       16 CALLS          17 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  -9.22919e+00
   2  a1           2.00000e-01   1.00000e-01   2.57889e-01   3.56932e+01
   3  bkgfrac      5.00000e-01   1.00000e-01   2.01358e-01   2.47046e+01
   4  sig1frac     8.00000e-01   1.00000e-01   2.57889e-01   9.71383e+00
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=104.639 FROM MIGRAD    STATUS=CONVERGED      78 CALLS          79 TOTAL
                     EDM=5.30614e-06    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  a0           5.00975e-01   2.29160e-02   2.25835e-04  -3.66627e-02
   2  a1           1.58055e-01   3.68598e-02   3.29973e-04   9.16128e-03
   3  bkgfrac      5.06726e-01   1.13595e-02   6.50594e-05   4.90783e-02
   4  sig1frac     8.16064e-01   3.74255e-02   3.05383e-04  -3.32372e-02
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=1
  5.255e-04  1.573e-04 -3.988e-05 -1.315e-04 
  1.573e-04  1.363e-03 -3.100e-04 -9.244e-04 
 -3.988e-05 -3.100e-04  1.291e-04  3.237e-04 
 -1.315e-04 -9.244e-04  3.237e-04  1.405e-03 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3      4
        1  0.18992   1.000  0.186 -0.153 -0.153
        2  0.75966   0.186  1.000 -0.739 -0.668
        3  0.82130  -0.153 -0.739  1.000  0.760
        4  0.77660  -0.153 -0.668  0.760  1.000
 **********
 **    7 **SET ERR           1
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        2000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=104.639 FROM HESSE     STATUS=OK             23 CALLS         102 TOTAL
                     EDM=5.30457e-06    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  a0           5.00975e-01   2.29157e-02   4.51671e-05   1.95002e-03
   2  a1           1.58055e-01   3.68515e-02   6.59945e-05  -7.53081e-01
   3  bkgfrac      5.06726e-01   1.13574e-02   1.30119e-05   1.34521e-02
   4  sig1frac     8.16064e-01   3.74193e-02   6.10765e-05   6.84296e-01
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  4    ERR DEF=1
  5.255e-04  1.572e-04 -3.986e-05 -1.314e-04 
  1.572e-04  1.363e-03 -3.098e-04 -9.239e-04 
 -3.986e-05 -3.098e-04  1.290e-04  3.236e-04 
 -1.314e-04 -9.239e-04  3.236e-04  1.405e-03 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3      4
        1  0.18986   1.000  0.186 -0.153 -0.153
        2  0.75953   0.186  1.000 -0.739 -0.668
        3  0.82122  -0.153 -0.739  1.000  0.760
        4  0.77651  -0.153 -0.668  0.760  1.000
29.4863

 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooChebychev.h"
#include "RooAddPdf.h"
#include "RooChi2Var.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit;
 
void rf602_chi2fit()
{
 
   // S e t u p   m o d e l
   // ---------------------
 
   // 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 pdf
   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 pdf
   RooRealVar sig1frac("sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.);
   RooAddPdf sig("sig", "Signal", RooArgList(sig1, sig2), sig1frac);
 
   // Sum the composite signal and background
   RooRealVar bkgfrac("bkgfrac", "fraction of background", 0.5, 0., 1.);
   RooAddPdf model("model", "g1+g2+a", RooArgList(bkg, sig), bkgfrac);
 
   // C r e a t e   b i n n e d   d a t a s e t
   // -----------------------------------------
 
   RooDataSet *d = model.generate(x, 10000);
   RooDataHist *dh = d->binnedClone();
 
   // Construct a chi^2 of the data and the model.
   // When a pdf is used in a chi^2 fit, the probability density scaled
   // by the number of events in the dataset to obtain the fit function
   // If model is an extended pdf, the expected number events is used
   // instead of the observed number of events.
   model.chi2FitTo(*dh);
 
   // NB: It is also possible to fit a RooAbsReal function to a RooDataHist
   // using chi2FitTo().
 
   // Note that entries with zero bins are _not_ allowed
   // for a proper chi^2 calculation and will give error
   // messages
   RooDataSet *dsmall = (RooDataSet *)d->reduce(EventRange(1, 100));
   RooDataHist *dhsmall = dsmall->binnedClone();
   RooChi2Var chi2_lowstat("chi2_lowstat", "chi2", model, *dhsmall);
   cout << chi2_lowstat.getVal() << endl;
}

Date

July 2008

Author

Wouter Verkerke

Definition in file rf602_chi2fit.C.