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
   std::unique_ptr<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
 
   std::unique_ptr<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
   std::unique_ptr<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();
}

 
[#0] WARNING:InputArguments -- The parameter 'sigma_g1' with range [-inf, inf] of the RooGaussian 'g1' exceeds the safe range of (0, inf). Advise to limit its range.
[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Fitting -- using CPU computation library compiled with -mavx2
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level
Minuit2Minimizer: Minimize with max-calls 1500 convergence for edm < 1 strategy 1
Minuit2Minimizer : Valid minimum - status = 0
FVAL  = 2659.73712858695399
Edm   = 0.000190395763129910388
Nfcn  = 60
frac    = 0.62118  +/-  0.165788 (limited)
mean    = 0.00442366  +/-  0.109372 (limited)
sigma_g2   = 4.10789  +/-  0.405468 (limited)
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[frac]) Creating instance of MINUIT
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[frac]) determining minimum likelihood for current configurations w.r.t all observable
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[frac]) minimum found at (frac=0.62104)
..................................................................................
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[sigma_g2]) Creating instance of MINUIT
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[sigma_g2]) determining minimum likelihood for current configurations w.r.t all observable
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[sigma_g2]) minimum found at (sigma_g2=4.11258)
....................................................................................

Date

July 2008

Author

Wouter Verkerke

Definition in file rf605_profilell.C.