rf202_extendedmlfit.C File Reference

Detailed Description

Setting up an extended maximum likelihood fit.

 
 
␛[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.
[#1] INFO:Minimization -- p.d.f. provides expected number of events, including extended term in likelihood.
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
[#1] INFO:Minimization --  The following expressions have been identified as constant and will be precalculated and cached: (sig1,sig2)
[#1] INFO:Minimization --  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   6.32307e-03
   5  sig1frac     8.37341e-01   1.17266e-01   8.52165e-03  -5.56323e-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:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg,sig2)
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: (sig)
0x7ffd606ee538 RooAddPdf::model = 0.898614/1 [Auto,Clean] 
  0x7ffd606ef030/V- RooChebychev::bkg = 0.798919 [Auto,Dirty] 
    0x7ffd606eec48/V- RooRealVar::x = 5
    0x7ffd606f0fe8/V- RooRealVar::a0 = 0.441701 +/- 0.073185
    0x7ffd606f0c00/V- RooRealVar::a1 = 0.201081 +/- 0.117613
  0x7ffd606ef550/V- RooRealVar::nbkg = 504.206 +/- 39.3107
  0x7ffd606f0108/V- RooAddPdf::sig = 1/1 [Auto,Clean] 
    0x7ffd606f20f0/V- RooGaussian::sig1 = 1 [Auto,Dirty] 
      0x7ffd606eec48/V- RooRealVar::x = 5
      0x7ffd606efd20/V- RooRealVar::mean = 5
      0x7ffd606f17b8/V- RooRealVar::sigma1 = 0.5
    0x7ffd606f0818/V- RooRealVar::sig1frac = 0.837341 +/- 0.116841
    0x7ffd606f1ba0/V- RooGaussian::sig2 = 1 [Auto,Dirty] 
      0x7ffd606eec48/V- RooRealVar::x = 5
      0x7ffd606efd20/V- RooRealVar::mean = 5
      0x7ffd606f13d0/V- RooRealVar::sigma2 = 1
  0x7ffd606ef938/V- RooRealVar::nsig = 495.799 +/- 39.2054

 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooAddPdf.h"
#include "RooExtendPdf.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit;
 
void rf202_extendedmlfit()
{
 
   // 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 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);
 
   //----------------
   // M E T H O D   1
   //================
 
   // C o n s t r u c t   e x t e n d e d   c o m p o s i t e   m o d e l
   // -------------------------------------------------------------------
 
   // Sum the composite signal and background into an extended pdf nsig*sig+nbkg*bkg
   RooRealVar nsig("nsig", "number of signal events", 500, 0., 10000);
   RooRealVar nbkg("nbkg", "number of background events", 500, 0, 10000);
   RooAddPdf model("model", "(g1+g2)+a", RooArgList(bkg, sig), RooArgList(nbkg, nsig));
 
   // S a m p l e ,   f i t   a n d   p l o t   e x t e n d e d   m o d e l
   // ---------------------------------------------------------------------
 
   // Generate a data sample of expected number events in x from model
   // = model.expectedEvents() = nsig+nbkg
   RooDataSet *data = model.generate(x);
 
   // Fit model to data, extended ML term automatically included
   model.fitTo(*data);
 
   // Plot data and PDF overlaid, use expected number of events for pdf projection normalization
   // rather than observed number of events (==data->numEntries())
   RooPlot *xframe = x.frame(Title("extended ML fit example"));
   data->plotOn(xframe);
   model.plotOn(xframe, Normalization(1.0, RooAbsReal::RelativeExpected));
 
   // Overlay the background component of model with a dashed line
   model.plotOn(xframe, Components(bkg), LineStyle(kDashed), Normalization(1.0, RooAbsReal::RelativeExpected));
 
   // Overlay the background+sig2 components of model with a dotted line
   model.plotOn(xframe, Components(RooArgSet(bkg, sig2)), LineStyle(kDotted),
                Normalization(1.0, RooAbsReal::RelativeExpected));
 
   // Print structure of composite pdf
   model.Print("t");
 
   //----------------
   // M E T H O D   2
   //================
 
   // C o n s t r u c t   e x t e n d e d   c o m p o n e n t s   f i r s t
   // ---------------------------------------------------------------------
 
   // Associated nsig/nbkg as expected number of events with sig/bkg
   RooExtendPdf esig("esig", "extended signal pdf", sig, nsig);
   RooExtendPdf ebkg("ebkg", "extended background pdf", bkg, nbkg);
 
   // S u m   e x t e n d e d   c o m p o n e n t s   w i t h o u t   c o e f s
   // -------------------------------------------------------------------------
 
   // Construct sum of two extended pdf (no coefficients required)
   RooAddPdf model2("model2", "(g1+g2)+a", RooArgList(ebkg, esig));
 
   // Draw the frame on the canvas
   new TCanvas("rf202_composite", "rf202_composite", 600, 600);
   gPad->SetLeftMargin(0.15);
   xframe->GetYaxis()->SetTitleOffset(1.4);
   xframe->Draw();
}

Date

July 2008

Author

Wouter Verkerke

Definition in file rf202_extendedmlfit.C.