# Rf 2 0 4A_Extended Likelihood¶

Extended maximum likelihood fit in multiple ranges.

When an extended pdf and multiple ranges are used, the RooExtendPdf cannot correctly interpret the coefficients used for extension. This can be solved by using a RooAddPdf for extending the model.

Author: Stephan Hageboeck
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Saturday, November 28, 2020 at 10:40 AM.

In [1]:
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooExtendPdf.h"
#include "RooFitResult.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;


## Setup component pdfs¶

Declare observable x

In [2]:
RooRealVar x("x","x",0,11) ;

RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University



Create two gaussian pdfs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters

In [3]:
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) ;

[#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.


Build chebychev polynomial pdf

In [4]:
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

In [5]:
RooRealVar sig1frac("sig1frac","fraction of component 1 in signal",0.8,0.,1.) ;


## Extend the pdfs¶

Define signal range in which events counts are to be defined

In [6]:
x.setRange("signalRange",4,6) ;

[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'signalRange' created with bounds [4,6]


Associated nsig/nbkg as expected number of events with sig/bkg _in_therange "signalrange"

In [7]:
RooRealVar nsig("nsig","number of signal events in signalRange",500,0.,10000) ;
RooRealVar nbkg("nbkg","number of background events in signalRange",500,0,10000) ;


Use addpdf to extend the model. giving as many coefficients as pdfs switches on extension.

In [8]:
RooAddPdf  model("model","(g1+g2)+a", RooArgList(bkg,sig), RooArgList(nbkg,nsig)) ;


## Sample data, fit model¶

Generate 1000 events from model so that nsig,nbkg come out to numbers <<500 in fit

In [9]:
RooDataSet *data = model.generate(x,1000) ;

auto canv = new TCanvas("Canvas", "Canvas", 1500, 600);
canv->Divide(3,1);


## Fit full range¶

In [10]:
canv->cd(1);


Perform unbinned ml fit to data, full range

Important: The model needs to be copied when fitting with different ranges because the interpretation of the coefficients is tied to the fit range that's used in the first fit

In [11]:
RooAddPdf model1(model);
RooFitResult* r = model1.fitTo(*data,Save()) ;
r->Print() ;

RooPlot * frame = x.frame(Title("Full range fitted"));
data->plotOn(frame);
model1.plotOn(frame, VisualizeError(*r));
model1.plotOn(frame);
model1.paramOn(frame);
frame->Draw();

[#1] INFO:Minization -- p.d.f. provides expected number of events, including extended term in likelihood.
[#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] INFO:Minization --  The following expressions will be evaluated in cache-and-track mode: (bkg)
**********
**    1 **SET PRINT           1
**********
**********
**********
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
**********
**********
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=-3871.89 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   6.22718e+00
2  a1           2.00000e-01   1.00000e-01   2.57889e-01  -1.46786e+00
3  nbkg         5.00000e+02   2.50000e+02   1.18625e-01   3.78614e+00
4  nsig         5.00000e+02   2.50000e+02   1.18625e-01  -3.78710e+00
5  sig1frac     8.00000e-01   1.00000e-01   2.57889e-01  -2.60731e+00
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-3872.49 FROM MIGRAD    STATUS=CONVERGED      92 CALLS          93 TOTAL
EDM=8.63054e-05    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a0           4.26471e-01   7.58981e-02   6.35013e-03   2.23263e-02
2  a1           1.75944e-01   1.10401e-01   8.49976e-03  -2.48705e-02
3  nbkg         5.11008e+02   3.60346e+01   4.85975e-04  -2.28107e-01
4  nsig         4.88988e+02   3.57357e+01   4.87261e-04   2.14226e-01
5  sig1frac     8.63918e-01   1.08330e-01   8.79881e-03  -1.87106e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  5    ERR DEF=0.5
5.806e-03  2.284e-03 -6.486e-01  6.487e-01 -2.172e-03
2.284e-03  1.255e-02 -2.540e+00  2.540e+00 -8.020e-03
-6.486e-01 -2.540e+00  1.299e+03 -7.878e+02  2.592e+00
6.487e-01  2.540e+00 -7.878e+02  1.277e+03 -2.593e+00
-2.172e-03 -8.020e-03  2.592e+00 -2.593e+00  1.215e-02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4      5
1  0.29577   1.000  0.268 -0.236  0.238 -0.259
2  0.73433   0.268  1.000 -0.629  0.635 -0.650
3  0.72344  -0.236 -0.629  1.000 -0.612  0.653
4  0.72920   0.238  0.635 -0.612  1.000 -0.658
5  0.75608  -0.259 -0.650  0.653 -0.658  1.000
**********
**    7 **SET ERR         0.5
**********
**********
**    8 **SET PRINT           1
**********
**********
**    9 **HESSE        2500
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-3872.49 FROM HESSE     STATUS=OK             31 CALLS         124 TOTAL
EDM=8.60976e-05    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  a0           4.26471e-01   7.58562e-02   1.27003e-03  -1.47593e-01
2  a1           1.75944e-01   1.10000e-01   1.69995e-03  -7.05103e-01
3  nbkg         5.11008e+02   3.59610e+01   9.71951e-05  -1.11474e+00
4  nsig         4.88988e+02   3.56576e+01   9.74523e-05  -1.12485e+00
5  sig1frac     8.63918e-01   1.08098e-01   1.75976e-03   8.15160e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  5    ERR DEF=0.5
5.800e-03  2.258e-03 -6.425e-01  6.425e-01 -2.152e-03
2.258e-03  1.245e-02 -2.515e+00  2.516e+00 -7.942e-03
-6.425e-01 -2.515e+00  1.293e+03 -7.824e+02  2.576e+00
6.425e-01  2.516e+00 -7.824e+02  1.272e+03 -2.576e+00
-2.152e-03 -7.942e-03  2.576e+00 -2.576e+00  1.209e-02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4      5
1  0.29405   1.000  0.266 -0.235  0.237 -0.257
2  0.73196   0.266  1.000 -0.627  0.632 -0.647
3  0.72209  -0.235 -0.627  1.000 -0.610  0.651
4  0.72779   0.237  0.632 -0.610  1.000 -0.657
5  0.75482  -0.257 -0.647  0.651 -0.657  1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization

RooFitResult: minimized FCN value: -3872.49, estimated distance to minimum: 8.60976e-05
covariance matrix quality: Full, accurate covariance matrix
Status : MINIMIZE=0 HESSE=0

Floating Parameter    FinalValue +/-  Error
--------------------  --------------------------
a0    4.2647e-01 +/-  7.59e-02
a1    1.7594e-01 +/-  1.10e-01
nbkg    5.1101e+02 +/-  3.60e+01
nsig    4.8899e+02 +/-  3.57e+01
sig1frac    8.6392e-01 +/-  1.08e-01



## Fit in two regions¶

In [12]:
canv->cd(2);
x.setRange("left",  0., 4.);
x.setRange("right", 6., 10.);

RooFitResult* r2 = model2.fitTo(*data,
Range("left,right"),
Save()) ;
r2->Print();

RooPlot * frame2 = x.frame(Title("Fit in left/right sideband"));
data->plotOn(frame2);
model2.plotOn(frame2, VisualizeError(*r2));
model2.plotOn(frame2);
model2.paramOn(frame2);
frame2->Draw();

[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'left' created with bounds [0,4]
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'right' created with bounds [6,10]
[#1] INFO:Minization -- p.d.f. provides expected number of events, including extended term in likelihood.
[#1] INFO:Fitting -- RooAbsOptTestStatistic::ctor(nll_model_modelData_left) constructing test statistic for sub-range named left
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'NormalizationRangeForleft' created with bounds [0,11]
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData_left' created with bounds [0,4]
[#1] INFO:Fitting -- RooAbsOptTestStatistic::ctor(nll_model_modelData_left) fixing interpretation of coefficients of any RooAddPdf to full domain of observables
[#1] INFO:Fitting -- RooAbsOptTestStatistic::ctor(nll_model_modelData_right) constructing test statistic for sub-range named right
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'NormalizationRangeForright' created with bounds [0,11]
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData_right' created with bounds [6,10]
[#1] INFO:Fitting -- RooAbsOptTestStatistic::ctor(nll_model_modelData_right) fixing interpretation of coefficients of any RooAddPdf to full domain of observables
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level
[#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] INFO:Minization --  The following expressions will be evaluated in cache-and-track mode: (bkg)
[#1] INFO:Minization --  The following expressions have been identified as constant and will be precalculated and cached: (sig1,sig2)
[#1] INFO:Minization --  The following expressions will be evaluated in cache-and-track mode: (bkg)
**********
**   10 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a0           4.26471e-01  7.58562e-02    0.00000e+00  1.00000e+00
2 a1           1.75944e-01  1.10000e-01    0.00000e+00  1.00000e+00
3 nbkg         5.11008e+02  3.59610e+01    0.00000e+00  1.00000e+04
4 nsig         4.88988e+02  3.56576e+01    0.00000e+00  1.00000e+04
5 sig1frac     8.63918e-01  1.08098e-01    0.00000e+00  1.00000e+00
**********
**   12 **SET ERR         0.5
**********
**********
**   13 **SET PRINT           1
**********
**********
**   14 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**********
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=-1133.19 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           4.26471e-01   7.58562e-02   1.54029e-01   2.97025e+00
2  a1           1.75944e-01   1.10000e-01   3.04490e-01   3.05683e+00
3  nbkg         5.11008e+02   3.59610e+01   1.63406e-02   4.24214e+01
4  nsig         4.88988e+02   3.56576e+01   1.65451e-02   5.45919e-01
5  sig1frac     8.63918e-01   1.08098e-01   3.48778e-01   7.27615e-01
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-1134.15 FROM MIGRAD    STATUS=CONVERGED     149 CALLS         150 TOTAL
EDM=1.94982e-05    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a0           3.23929e-01   1.10404e-01   4.10351e-03   8.17015e-03
2  a1           2.88453e-02   5.45830e-01   1.39787e-02  -5.49618e-03
3  nbkg         5.01892e+02   3.98714e+01   2.93870e-04  -1.33300e-01
4  nsig         4.10983e+02   2.63611e+02   1.44231e-03  -6.59247e-03
5  sig1frac     8.58940e-01   2.76155e-01   7.42299e-03   1.70743e-03
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  5    ERR DEF=0.5
1.242e-02  1.300e-02 -1.353e+00 -5.302e+00 -1.528e-02
1.300e-02  3.091e-02 -3.948e+00 -1.123e+01 -3.495e-02
-1.353e+00 -3.948e+00  1.590e+03  2.791e+03  7.770e+00
-5.302e+00 -1.123e+01  2.791e+03  6.990e+04  6.730e+01
-1.528e-02 -3.495e-02  7.770e+00  6.730e+01  1.017e-01
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4      5
1  0.67241   1.000  0.664 -0.304 -0.180 -0.430
2  0.82439   0.664  1.000 -0.563 -0.242 -0.623
3  0.72220  -0.304 -0.563  1.000  0.265  0.611
4  0.88430  -0.180 -0.242  0.265  1.000  0.798
5  0.93740  -0.430 -0.623  0.611  0.798  1.000
**********
**   16 **SET ERR         0.5
**********
**********
**   17 **SET PRINT           1
**********
**********
**   18 **HESSE        2500
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-1134.15 FROM HESSE     STATUS=OK             31 CALLS         181 TOTAL
EDM=1.87887e-05    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  a0           3.23929e-01   1.08109e-01   8.20702e-04  -3.59858e-01
2  a1           2.88453e-02   5.40605e-01   5.59149e-04  -1.22946e+00
3  nbkg         5.01892e+02   3.94665e+01   5.87740e-05  -1.11890e+00
4  nsig         4.10983e+02   2.68023e+02   2.88462e-04  -1.16251e+00
5  sig1frac     8.58940e-01   2.76392e-01   2.96920e-04   8.00751e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  5    ERR DEF=0.5
1.190e-02  1.198e-02 -1.213e+00 -5.251e+00 -1.425e-02
1.198e-02  2.901e-02 -3.680e+00 -1.127e+01 -3.307e-02
-1.213e+00 -3.680e+00  1.558e+03  2.890e+03  7.605e+00
-5.251e+00 -1.127e+01  2.890e+03  7.228e+04  6.954e+01
-1.425e-02 -3.307e-02  7.605e+00  6.954e+01  1.020e-01
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4      5
1  0.65435   1.000  0.645 -0.282 -0.179 -0.409
2  0.81152   0.645  1.000 -0.547 -0.246 -0.608
3  0.71533  -0.282 -0.547  1.000  0.272  0.603
4  0.88834  -0.179 -0.246  0.272  1.000  0.810
5  0.93756  -0.409 -0.608  0.603  0.810  1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization

RooFitResult: minimized FCN value: -1134.15, estimated distance to minimum: 1.87887e-05
covariance matrix quality: Full, accurate covariance matrix
Status : MINIMIZE=0 HESSE=0

Floating Parameter    FinalValue +/-  Error
--------------------  --------------------------
a0    3.2393e-01 +/-  1.08e-01
a1    2.8845e-02 +/-  5.41e-01
nbkg    5.0189e+02 +/-  3.95e+01
nsig    4.1098e+02 +/-  2.68e+02
sig1frac    8.5894e-01 +/-  2.76e-01

[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f was fitted in a subrange and no explicit Range() and NormRange() was specified. Plotting / normalising in fit range. To override, do one of the following
- Clear the automatic fit range attribute: <pdf>.setStringAttribute("fitrange", nullptr);
- Explicitly specify the plotting range: Range("<rangeName>").
- Explicitly specify where to compute the normalisation: NormRange("<rangeName>").
The default (full) range can be denoted with Range("") / NormRange("").
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f was fitted in a subrange and no explicit Range() and NormRange() was specified. Plotting / normalising in fit range. To override, do one of the following
- Clear the automatic fit range attribute: <pdf>.setStringAttribute("fitrange", nullptr);
- Explicitly specify the plotting range: Range("<rangeName>").
- Explicitly specify where to compute the normalisation: NormRange("<rangeName>").
The default (full) range can be denoted with Range("") / NormRange("").
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData_left,fit_nll_model_modelData_right'


## Fit in one region¶

Note how restricting the region to only the left tail increases the fit uncertainty

In [13]:
canv->cd(3);
x.setRange("leftToMiddle",  0., 5.);

RooFitResult* r3 = model3.fitTo(*data,
Range("leftToMiddle"),
Save()) ;
r3->Print();

RooPlot * frame3 = x.frame(Title("Fit from left to middle"));
data->plotOn(frame3);
model3.plotOn(frame3, VisualizeError(*r3));
model3.plotOn(frame3);
model3.paramOn(frame3);
frame3->Draw();

canv->Draw();

[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'leftToMiddle' created with bounds [0,5]
[#1] INFO:Minization -- p.d.f. provides expected number of events, including extended term in likelihood.
[#1] INFO:Fitting -- RooAbsOptTestStatistic::ctor(nll_model_modelData) constructing test statistic for sub-range named leftToMiddle
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'NormalizationRangeForleftToMiddle' created with bounds [0,11]
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData' created with bounds [0,5]
[#1] INFO:Fitting -- RooAbsOptTestStatistic::ctor(nll_model_modelData) fixing interpretation of coefficients of any RooAddPdf to full domain of observables
[#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] INFO:Minization --  The following expressions will be evaluated in cache-and-track mode: (bkg)
**********
**   19 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 a0           3.23929e-01  1.08109e-01    0.00000e+00  1.00000e+00
2 a1           2.88453e-02  5.40605e-01    0.00000e+00  1.00000e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE2 BROUGHT BACK INSIDE LIMITS.
3 nbkg         5.01892e+02  3.94665e+01    0.00000e+00  1.00000e+04
4 nsig         4.10983e+02  2.68023e+02    0.00000e+00  1.00000e+04
5 sig1frac     8.58940e-01  2.76392e-01    0.00000e+00  1.00000e+00
MINUIT WARNING IN PARAMETR
============== VARIABLE5 BROUGHT BACK INSIDE LIMITS.
**********
**   21 **SET ERR         0.5
**********
**********
**   22 **SET PRINT           1
**********
**********
**   23 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**********
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=-1618.32 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           3.23929e-01   1.08109e-01   2.34083e-01   4.08551e-01
2  a1           2.88453e-02   5.40605e-01   8.54097e-01  -2.73477e-01
3  nbkg         5.01892e+02   3.94665e+01   1.80897e-02  -6.58003e+00
4  nsig         4.10983e+02   2.68023e+02   1.43768e-01  -1.02034e+02
5  sig1frac     8.58940e-01   2.76392e-01   7.01494e-01  -4.26596e+00
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-1.9268e-03  1.4073e-01  1.2202e+00  1.3132e+00  2.3278e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.004255 TO DIAGONAL.
FCN=-1620.15 FROM HESSE     STATUS=NOT POSDEF     35 CALLS         127 TOTAL
EDM=0.00100154    STRATEGY= 1      ERR MATRIX NOT POS-DEF
EXT PARAMETER                APPROXIMATE        STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a0           3.43232e-01   6.29734e-01   5.61952e-03  -2.08276e-02
2  a1           1.02853e-01   5.84687e-01   1.07156e-02   4.02420e-03
3  nbkg         4.96425e+02   5.58143e+02   5.33145e-04   4.79276e-02
4  nsig         4.64995e+02   7.12947e+01   4.44597e-04  -9.78209e-02
5  sig1frac     9.25999e-01   1.76430e-01   1.11400e-02  -7.64957e-03
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-1620.17 FROM MIGRAD    STATUS=CONVERGED     342 CALLS         343 TOTAL
EDM=0.000217441    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  a0           7.69361e-01   8.83057e-01   3.86565e-03  -2.13935e-02
2  a1           2.46425e-01   2.97584e-01   4.87451e-03  -2.30492e-02
3  nbkg         7.73200e+02   8.70057e+02   6.44465e-04   2.32139e-01
4  nsig         4.38086e+02   8.85580e+01   4.50255e-04  -8.74799e-02
5  sig1frac     9.85817e-01   8.72235e-01   2.19213e-02  -1.54609e-02
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  5    ERR DEF=0.5
7.281e-01  2.677e-01  7.525e+02 -6.291e+01  1.261e-01
2.677e-01  1.079e-01  2.722e+02 -2.028e+01  3.655e-02
7.525e+02  2.722e+02  7.854e+05 -6.768e+04  1.398e+02
-6.291e+01 -2.028e+01 -6.768e+04  7.847e+03 -1.635e+01
1.261e-01  3.655e-02  1.398e+02 -1.635e+01  4.920e-02
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4      5
1  0.99765   1.000  0.955  0.995 -0.832  0.666
2  0.97507   0.955  1.000  0.935 -0.697  0.502
3  0.99750   0.995  0.935  1.000 -0.862  0.711
4  0.92717  -0.832 -0.697 -0.862  1.000 -0.832
5  0.87584   0.666  0.502  0.711 -0.832  1.000
**********
**   25 **SET ERR         0.5
**********
**********
**   26 **SET PRINT           1
**********
**********
**   27 **HESSE        2500
**********
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-1620.17 FROM HESSE     STATUS=OK             31 CALLS         374 TOTAL
EDM=0.000231402    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                INTERNAL      INTERNAL
NO.   NAME      VALUE            ERROR       STEP SIZE       VALUE
1  a0           7.69361e-01   7.93367e-01   7.73130e-04   5.68919e-01
2  a1           2.46425e-01   6.23108e-01   9.74903e-04  -5.31876e-01
3  nbkg         7.73200e+02   1.28458e+03   1.28893e-04  -1.00724e+00
4  nsig         4.38086e+02   1.32094e+02   9.00510e-05  -1.14907e+00
5  sig1frac     9.85817e-01   9.88104e-01   8.76851e-04   1.33204e+00
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  5    ERR DEF=0.5
1.621e+00  5.715e-01  1.702e+03 -1.549e+02  3.399e-01
5.715e-01  2.117e-01  5.948e+02 -5.131e+01  1.082e-01
1.702e+03  5.948e+02  1.796e+06 -1.658e+05  3.682e+02
-1.549e+02 -5.131e+01 -1.658e+05  1.747e+04 -3.895e+01
3.399e-01  1.082e-01  3.682e+02 -3.895e+01  1.024e-01
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3      4      5
1  0.99894   1.000  0.975  0.998 -0.920  0.834
2  0.98737   0.975  1.000  0.965 -0.844  0.735
3  0.99891   0.998  0.965  1.000 -0.936  0.858
4  0.96797  -0.920 -0.844 -0.936  1.000 -0.921
5  0.94231   0.834  0.735  0.858 -0.921  1.000
[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization

RooFitResult: minimized FCN value: -1620.17, estimated distance to minimum: 0.000231402
covariance matrix quality: Full, accurate covariance matrix
Status : MINIMIZE=0 HESSE=0

Floating Parameter    FinalValue +/-  Error
--------------------  --------------------------
a0    7.6936e-01 +/-  7.93e-01
a1    2.4642e-01 +/-  6.23e-01
nbkg    7.7320e+02 +/-  1.28e+03
nsig    4.3809e+02 +/-  1.32e+02
sig1frac    9.8582e-01 +/-  9.88e-01

[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f was fitted in a subrange and no explicit Range() and NormRange() was specified. Plotting / normalising in fit range. To override, do one of the following
- Clear the automatic fit range attribute: <pdf>.setStringAttribute("fitrange", nullptr);
- Explicitly specify the plotting range: Range("<rangeName>").
- Explicitly specify where to compute the normalisation: NormRange("<rangeName>").
The default (full) range can be denoted with Range("") / NormRange("").
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f was fitted in a subrange and no explicit Range() and NormRange() was specified. Plotting / normalising in fit range. To override, do one of the following
- Clear the automatic fit range attribute: <pdf>.setStringAttribute("fitrange", nullptr);
- Explicitly specify the plotting range: Range("<rangeName>").
- Explicitly specify where to compute the normalisation: NormRange("<rangeName>").
The default (full) range can be denoted with Range("") / NormRange("").
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) only plotting range 'fit_nll_model_modelData'
[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) p.d.f. curve is normalized using explicit choice of ranges 'fit_nll_model_modelData'


Draw all canvases

In [14]:
%jsroot on
gROOT->GetListOfCanvases()->Draw()