rf606_nllerrorhandling.C File Reference

Detailed Description

Likelihood and minimization: understanding and customizing error handling in likelihood evaluations

 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooArgusBG.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit;
 
void rf606_nllerrorhandling()
{
   // C r e a t e   m o d e l  a n d   d a t a s e t
   // ----------------------------------------------
 
   // Observable
   RooRealVar m("m", "m", 5.20, 5.30);
 
   // Parameters
   RooRealVar m0("m0", "m0", 5.291, 5.20, 5.30);
   RooRealVar k("k", "k", -30, -50, -10);
 
   // Pdf
   RooArgusBG argus("argus", "argus", m, m0, k);
 
   // Sample 1000 events in m from argus
   RooDataSet *data = argus.generate(m, 1000);
 
   // P l o t   m o d e l   a n d   d a t a
   // --------------------------------------
 
   RooPlot *frame1 = m.frame(Bins(40), Title("Argus model and data"));
   data->plotOn(frame1);
   argus.plotOn(frame1);
 
   // F i t   m o d e l   t o   d a t a
   // ---------------------------------
 
   // The ARGUS background shape has a sharp kinematic cutoff at m=m0
   // and is prone to evaluation errors if the cutoff parameter m0
   // is floated: when the pdf cutoff value is lower than that in data
   // events with m>m0 will have zero probability
 
   // Perform unbinned ML fit. Print detailed error messages for up to
   // 10 events per likelihood evaluation. The default error handling strategy
   // is to return a very high value of the likelihood to MINUIT if errors occur,
   // which will force MINUIT to retreat from the problematic area
 
   argus.fitTo(*data, PrintEvalErrors(10));
 
   // Perform another fit. In this configuration only the number of errors per
   // likelihood evaluation is shown, if it is greater than zero. The
   // EvalErrorWall(false) arguments disables the default error handling strategy
   // and will cause the actual (problematic) value of the likelihood to be passed
   // to MINUIT.
   //
   // NB: Use of this option is NOT recommended as default strategy as broken -log(L) values
   // can often be lower than 'good' ones because offending events are removed.
   // This may effectively create a false minimum in problem areas. This is clearly
   // illustrated in the second plot
 
   m0.setError(0.1);
   argus.fitTo(*data, PrintEvalErrors(0), EvalErrorWall(false));
 
   // P l o t   l i k e l i h o o d   a s   f u n c t i o n   o f   m 0
   // ------------------------------------------------------------------
 
   // Construct likelihood function of model and data
   std::unique_ptr<RooAbsReal> nll{argus.createNLL(*data)};
 
   // Plot likelihood in m0 in range that includes problematic values
   // In this configuration no messages are printed for likelihood evaluation errors,
   // but if an likelihood value evaluates with error, the corresponding value
   // on the curve will be set to the value given in EvalErrorValue().
 
   RooPlot *frame2 = m0.frame(Range(5.288, 5.293), Title("-log(L) scan vs m0, problematic regions masked"));
   nll->plotOn(frame2, PrintEvalErrors(-1), ShiftToZero(), EvalErrorValue(nll->getVal() + 10), LineColor(kRed));
   frame2->SetMaximum(15);
   frame2->SetMinimum(0);
 
   TCanvas *c = new TCanvas("rf606_nllerrorhandling", "rf606_nllerrorhandling", 1200, 400);
   c->Divide(2);
   c->cd(1);
   gPad->SetLeftMargin(0.15);
   frame1->GetYaxis()->SetTitleOffset(1.4);
   frame1->Draw();
   c->cd(2);
   gPad->SetLeftMargin(0.15);
   frame2->GetYaxis()->SetTitleOffset(1.4);
   frame2->Draw();
}

 
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 k           -3.00000e+01  4.00000e+00   -5.00000e+01 -1.00000e+01
     2 m0           5.29100e+00  4.50000e-03    5.20000e+00  5.30000e+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        1000           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=-2417.48 FROM MIGRAD    STATUS=INITIATE        6 CALLS           7 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  k           -3.00000e+01   4.00000e+00   2.01358e-01   6.43007e+00
   2  m0           5.29100e+00   4.50000e-03   1.62481e-01   6.64912e+01
                               ERR DEF= 0.5
RooAbsMinimizerFcn: Minimized function has error status.
Returning maximum FCN so far (-2417.21) to force MIGRAD to back out of this region. Error log follows.
Parameter values:    k=-33.8074  m0=5.29014
RooArgusBG::argus[ m=m m0=m0 c=k p=0.5 ]
     getLogVal() top-level p.d.f evaluates to zero @ m=m=5.29019, m0=m0=5.29014, c=k=-33.8074, p=0.5=0.5
RooNLLVar::nll_argus_argusData[ parameters=(k,m0) ]
     function value is NAN @ parameters=(k = -33.8074,m0 = 5.29014)
 
RooAbsMinimizerFcn: Minimized function has error status.
Returning maximum FCN so far (-2417.21) to force MIGRAD to back out of this region. Error log follows.
Parameter values:    k=-36.6878  m0=5.29012
RooArgusBG::argus[ m=m m0=m0 c=k p=0.5 ]
     getLogVal() top-level p.d.f evaluates to zero @ m=m=5.29019, m0=m0=5.29012, c=k=-36.6878, p=0.5=0.5
RooNLLVar::nll_argus_argusData[ parameters=(k,m0) ]
     function value is NAN @ parameters=(k = -36.6878,m0 = 5.29012)
 
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=-2419.31 FROM MIGRAD    STATUS=CONVERGED      44 CALLS          45 TOTAL
                     EDM=1.16119e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  k           -3.53724e+01   3.51965e+00   6.12703e-03  -1.66396e-02
   2  m0           5.29040e+00   2.62256e-04   3.09448e-04   2.47503e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  1.253e+01  1.785e-04 
  1.785e-04  6.878e-08 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.19224   1.000  0.192
        2  0.19224   0.192  1.000
 **********
 **    7 **SET ERR         0.5
 **********
 **********
 **    8 **SET PRINT           1
 **********
 **********
 **    9 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=-2419.31 FROM HESSE     STATUS=OK             10 CALLS          55 TOTAL
                     EDM=1.16219e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  k           -3.53724e+01   3.51966e+00   1.22541e-03  -2.71960e-01
   2  m0           5.29040e+00   2.62349e-04   1.23779e-05   9.40810e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  1.253e+01  1.786e-04 
  1.786e-04  6.883e-08 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.19229   1.000  0.192
        2  0.19229   0.192  1.000
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
 **********
 **   10 **SET PRINT           1
 **********
 **********
 **   11 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 k           -3.53724e+01  3.51966e+00   -5.00000e+01 -1.00000e+01
     2 m0           5.29040e+00  1.00000e-01    5.20000e+00  5.30000e+00
 MINUIT WARNING IN PARAMETR
 ============== VARIABLE2 BROUGHT BACK INSIDE LIMITS.
 MINUIT WARNING IN PARAMETR
 ============== VARIABLE2 BROUGHT BACK INSIDE LIMITS.
 **********
 **   12 **SET ERR         0.5
 **********
 **********
 **   13 **SET PRINT           1
 **********
 **********
 **   14 **SET STR           1
 **********
 NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
 **********
 **   15 **MIGRAD        1000           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
RooAbsMinimizerFcn: Minimized function has error status but is ignored.
Parameter values:    k=-35.3724  m0=5.28878
RooArgusBG::argus[ m=m m0=m0 c=k p=0.5 ] has 4 errors
RooNLLVar::nll_argus_argusData[ parameters=(k,m0) ] has 1 errors
 
 FCN=-2419.31 FROM MIGRAD    STATUS=INITIATE        8 CALLS           9 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  k           -3.53724e+01   3.51966e+00   1.83981e-01  -1.64778e-02
   2  m0           5.29040e+00   1.00000e-01   1.56884e+00   1.11846e-01
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=-2419.31 FROM MIGRAD    STATUS=CONVERGED      28 CALLS          29 TOTAL
                     EDM=4.57045e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  k           -3.53621e+01   3.51925e+00   6.12459e-03   8.76390e-04
   2  m0           5.29040e+00   2.62011e-04   2.96587e-04   7.04254e-02
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  1.253e+01  1.781e-04 
  1.781e-04  6.865e-08 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.19204   1.000  0.192
        2  0.19204   0.192  1.000
 **********
 **   16 **SET ERR         0.5
 **********
 **********
 **   17 **SET PRINT           1
 **********
 **********
 **   18 **HESSE        1000
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=-2419.31 FROM HESSE     STATUS=OK             10 CALLS          39 TOTAL
                     EDM=4.58038e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                INTERNAL      INTERNAL  
  NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE   
   1  k           -3.53621e+01   3.51925e+00   2.44984e-04  -2.71425e-01
   2  m0           5.29040e+00   2.62096e-04   1.18635e-05   9.40801e-01
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  2    ERR DEF=0.5
  1.253e+01  1.782e-04 
  1.782e-04  6.870e-08 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2
        1  0.19207   1.000  0.192
        2  0.19207   0.192  1.000
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization

Date

July 2008

Author

Wouter Verkerke

Definition in file rf606_nllerrorhandling.C.