rf605_profilell.C File Reference

Detailed Description

Likelihood and minimization: working with the profile likelihood estimator

 
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooAddPdf.h"
#include "RooMinimizer.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit;
 
void rf605_profilell()
{
   // C r e a t e   m o d e l   a n d   d a t a s e t
   // -----------------------------------------------
 
   // Observable
   RooRealVar x("x", "x", -20, 20);
 
   // Model (intentional strong correlations)
   RooRealVar mean("mean", "mean of g1 and g2", 0, -10, 10);
   RooRealVar sigma_g1("sigma_g1", "width of g1", 3);
   RooGaussian g1("g1", "g1", x, mean, sigma_g1);
 
   RooRealVar sigma_g2("sigma_g2", "width of g2", 4, 3.0, 6.0);
   RooGaussian g2("g2", "g2", x, mean, sigma_g2);
 
   RooRealVar frac("frac", "frac", 0.5, 0.0, 1.0);
   RooAddPdf model("model", "model", RooArgList(g1, g2), frac);
 
   // Generate 1000 events
   RooDataSet *data = model.generate(x, 1000);
 
   // C o n s t r u c t   p l a i n   l i k e l i h o o d
   // ---------------------------------------------------
 
   // Construct unbinned likelihood
   std::unique_ptr<RooAbsReal> nll{model.createNLL(*data, NumCPU(2))};
 
   // Minimize likelihood w.r.t all parameters before making plots
   RooMinimizer(*nll).migrad();
 
   // Plot likelihood scan frac
   RooPlot *frame1 = frac.frame(Bins(10), Range(0.01, 0.95), Title("LL and profileLL in frac"));
   nll->plotOn(frame1, ShiftToZero());
 
   // Plot likelihood scan in sigma_g2
   RooPlot *frame2 = sigma_g2.frame(Bins(10), Range(3.3, 5.0), Title("LL and profileLL in sigma_g2"));
   nll->plotOn(frame2, ShiftToZero());
 
   // C o n s t r u c t   p r o f i l e   l i k e l i h o o d   i n   f r a c
   // -----------------------------------------------------------------------
 
   // The profile likelihood estimator on nll for frac will minimize nll w.r.t
   // all floating parameters except frac for each evaluation
 
   RooAbsReal *pll_frac = nll->createProfile(frac);
 
   // Plot the profile likelihood in frac
   pll_frac->plotOn(frame1, LineColor(kRed));
 
   // Adjust frame maximum for visual clarity
   frame1->SetMinimum(0);
   frame1->SetMaximum(3);
 
   // C o n s t r u c t   p r o f i l e   l i k e l i h o o d   i n   s i g m a _ g 2
   // -------------------------------------------------------------------------------
 
   // The profile likelihood estimator on nll for sigma_g2 will minimize nll
   // w.r.t all floating parameters except sigma_g2 for each evaluation
   RooAbsReal *pll_sigmag2 = nll->createProfile(sigma_g2);
 
   // Plot the profile likelihood in sigma_g2
   pll_sigmag2->plotOn(frame2, LineColor(kRed));
 
   // Adjust frame maximum for visual clarity
   frame2->SetMinimum(0);
   frame2->SetMaximum(3);
 
   // Make canvas and draw RooPlots
   TCanvas *c = new TCanvas("rf605_profilell", "rf605_profilell", 800, 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();
 
   delete pll_frac;
   delete pll_sigmag2;
}

 
[#0] WARNING:InputArguments -- The parameter 'sigma_g1' with range [-1e+30, 1e+30] of the RooGaussian 'g1' exceeds the safe range of (0, inf). Advise to limit its range.
 **********
 **    1 **SET PRINT           1
 **********
 **********
 **    2 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 frac         5.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
     2 mean         0.00000e+00  2.00000e+00   -1.00000e+01  1.00000e+01
     3 sigma_g2     4.00000e+00  3.00000e-01    3.00000e+00  6.00000e+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        1500           1
 **********
 FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.
 START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
 FCN=2660.22 FROM MIGRAD    STATUS=INITIATE       10 CALLS          11 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  frac         5.00000e-01   1.00000e-01   2.01358e-01  -5.61980e+00
   2  mean         0.00000e+00   2.00000e+00   2.01358e-01  -7.16779e+00
   3  sigma_g2     4.00000e+00   3.00000e-01   2.14402e-01   7.28535e+00
                               ERR DEF= 0.5
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=2659.74 FROM MIGRAD    STATUS=CONVERGED      67 CALLS          68 TOTAL
                     EDM=5.19798e-06    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  frac         6.23972e-01   1.64510e-01   5.33134e-03   6.83204e-03
   2  mean         4.57491e-03   1.09369e-01   3.87767e-04  -1.84350e-01
   3  sigma_g2     4.11576e+00   4.07375e-01   4.33560e-03  -6.97269e-03
                               ERR DEF= 0.5
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  3    ERR DEF=0.5
  2.817e-02 -1.610e-03  6.258e-02 
 -1.610e-03  1.196e-02 -4.302e-03 
  6.258e-02 -4.302e-03  1.705e-01 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3
        1  0.90293   1.000 -0.088  0.903
        2  0.09533  -0.088  1.000 -0.095
        3  0.90308   0.903 -0.095  1.000
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[frac]) Creating instance of MINUIT
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[frac]) determining minimum likelihood for current configurations w.r.t all observable
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[frac]) minimum found at (frac=0.623915)
..................................................................................
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[sigma_g2]) Creating instance of MINUIT
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[sigma_g2]) determining minimum likelihood for current configurations w.r.t all observable
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[sigma_g2]) minimum found at (sigma_g2=4.11588)
....................................................................................

Date

July 2008

Author

Wouter Verkerke

Definition in file rf605_profilell.C.