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rf610_visualerror.C File Reference

Likelihood and minimization: visualization of errors from a covariance matrix

␛[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

[#1] INFO:Minization -- RooMinimizer::optimizeConst: activating const optimization

[#1] INFO:Minization -- The following expressions will be evaluated in cache-and-track mode: (sig,bkg)

**********

** 1 **SET PRINT 1

**********

**********

** 2 **SET NOGRAD

**********

PARAMETER DEFINITIONS:

NO. NAME VALUE STEP SIZE LIMITS

1 fsig 3.30000e-01 1.00000e-01 0.00000e+00 1.00000e+00

2 m 0.00000e+00 2.00000e+00 -1.00000e+01 1.00000e+01

3 m2 -1.00000e+00 2.00000e+00 -1.00000e+01 1.00000e+01

4 s 2.00000e+00 5.00000e-01 1.00000e+00 5.00000e+01

5 s2 6.00000e+00 2.50000e+00 1.00000e+00 5.00000e+01

**********

** 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=2770.05 FROM MIGRAD STATUS=INITIATE 20 CALLS 21 TOTAL

EDM= unknown STRATEGY= 1 NO ERROR MATRIX

EXT PARAMETER CURRENT GUESS STEP FIRST

NO. NAME VALUE ERROR SIZE DERIVATIVE

1 fsig 3.30000e-01 1.00000e-01 2.14988e-01 -9.80006e+00

2 m 0.00000e+00 2.00000e+00 2.01358e-01 -3.95919e+01

3 m2 -1.00000e+00 2.00000e+00 2.02430e-01 3.98515e+01

4 s 2.00000e+00 5.00000e-01 7.46809e-02 2.95415e+01

5 s2 6.00000e+00 2.50000e+00 1.74125e-01 4.56667e+01

ERR DEF= 0.5

MIGRAD MINIMIZATION HAS CONVERGED.

MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.

COVARIANCE MATRIX CALCULATED SUCCESSFULLY

FCN=2767.65 FROM MIGRAD STATUS=CONVERGED 125 CALLS 126 TOTAL

EDM=1.56678e-05 STRATEGY= 1 ERROR MATRIX ACCURATE

EXT PARAMETER STEP FIRST

NO. NAME VALUE ERROR SIZE DERIVATIVE

1 fsig 2.98883e-01 6.74303e-02 2.39863e-03 7.00359e-03

2 m 3.08816e-01 2.09098e-01 6.83546e-04 -2.93512e-02

3 m2 -1.31219e+00 3.64277e-01 9.46152e-04 8.97852e-02

4 s 1.78229e+00 2.51997e-01 9.25951e-04 -2.49363e-02

5 s2 5.51197e+00 4.85498e-01 6.94615e-04 1.27501e-01

ERR DEF= 0.5

EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 5 ERR DEF=0.5

4.580e-03 -3.800e-03 -1.557e-02 1.331e-02 2.642e-02

-3.800e-03 4.373e-02 -3.141e-03 -1.195e-02 -2.959e-02

-1.557e-02 -3.141e-03 1.328e-01 -4.509e-02 -1.100e-01

1.331e-02 -1.195e-02 -4.509e-02 6.354e-02 7.253e-02

2.642e-02 -2.959e-02 -1.100e-01 7.253e-02 2.358e-01

PARAMETER CORRELATION COEFFICIENTS

NO. GLOBAL 1 2 3 4 5

1 0.89430 1.000 -0.269 -0.632 0.780 0.804

2 0.43384 -0.269 1.000 -0.041 -0.227 -0.291

3 0.70478 -0.632 -0.041 1.000 -0.491 -0.621

4 0.78303 0.780 -0.227 -0.491 1.000 0.593

5 0.82883 0.804 -0.291 -0.621 0.593 1.000

**********

** 7 **SET ERR 0.5

**********

**********

** 8 **SET PRINT 1

**********

**********

** 9 **HESSE 2500

**********

COVARIANCE MATRIX CALCULATED SUCCESSFULLY

FCN=2767.65 FROM HESSE STATUS=OK 31 CALLS 157 TOTAL

EDM=1.56685e-05 STRATEGY= 1 ERROR MATRIX ACCURATE

EXT PARAMETER INTERNAL INTERNAL

NO. NAME VALUE ERROR STEP SIZE VALUE

1 fsig 2.98883e-01 6.78952e-02 4.79727e-04 -4.13956e-01

2 m 3.08816e-01 2.09026e-01 1.36709e-04 3.08865e-02

3 m2 -1.31219e+00 3.67042e-01 1.89230e-04 -1.31599e-01

4 s 1.78229e+00 2.53102e-01 1.85190e-04 -1.31741e+00

5 s2 5.51197e+00 4.89300e-01 1.38923e-04 -9.54177e-01

ERR DEF= 0.5

EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 5 ERR DEF=0.5

4.644e-03 -3.811e-03 -1.596e-02 1.350e-02 2.692e-02

-3.811e-03 4.370e-02 -2.970e-03 -1.206e-02 -2.967e-02

-1.596e-02 -2.970e-03 1.348e-01 -4.619e-02 -1.129e-01

1.350e-02 -1.206e-02 -4.619e-02 6.410e-02 7.402e-02

2.692e-02 -2.967e-02 -1.129e-01 7.402e-02 2.395e-01

PARAMETER CORRELATION COEFFICIENTS

NO. GLOBAL 1 2 3 4 5

1 0.89584 1.000 -0.268 -0.638 0.782 0.807

2 0.43319 -0.268 1.000 -0.039 -0.228 -0.290

3 0.71012 -0.638 -0.039 1.000 -0.497 -0.628

4 0.78518 0.782 -0.228 -0.497 1.000 0.597

5 0.83175 0.807 -0.290 -0.628 0.597 1.000

[#1] INFO:Minization -- RooMinimizer::optimizeConst: deactivating const optimization

[#0] WARNING:Plotting -- Fill color or style was set for plotting "model", but these only have an effect when 'DrawOption("F")' for fill is used at the same time.

[#0] WARNING:Plotting -- Fill color or style was set for plotting "model", but these only have an effect when 'DrawOption("F")' for fill is used at the same time.

[#0] WARNING:Plotting -- Fill color or style was set for plotting "model", but these only have an effect when 'DrawOption("F")' for fill is used at the same time.

[#1] INFO:Plotting -- RooAbsReal::plotOn(model) INFO: visualizing 1-sigma uncertainties in parameters (m,s,fsig,m2,s2) from fit result fitresult_model_genData using 315 samplings.

[#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)

[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()

[#1] INFO:Plotting -- RooAbsReal::plotOn(model) INFO: visualizing 1-sigma uncertainties in parameters (m,s,fsig,m2,s2) from fit result fitresult_model_genData using 315 samplings.

[#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)

[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()

[#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)

[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()

[#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)

[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()

[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) directly selected PDF components: (bkg)

[#1] INFO:Plotting -- RooAbsPdf::plotOn(model) indirectly selected PDF components: ()

#include "RooRealVar.h"

#include "RooDataHist.h"

#include "RooGaussian.h"

#include "RooConstVar.h"

#include "RooAddPdf.h"

#include "RooPlot.h"

#include "TCanvas.h"

#include "TAxis.h"

#include "TAxis.h"

using namespace RooFit;

void rf610_visualerror()

{

// S e t u p e x a m p l e f i t

// ---------------------------------------

// Create sum of two Gaussians pdf with factory

// Create binned dataset

x.setBins(25);

// Perform fit and save fit result

// V i s u a l i z e f i t e r r o r

// -------------------------------------

// Make plot frame

d->plotOn(frame);

// Visualize 1-sigma error encoded in fit result 'r' as orange band using linear error propagation

// This results in an error band that is by construction symmetric

//

// The linear error is calculated as

// error(x) = Z* F_a(x) * Corr(a,a') F_a'(x)

//

// where F_a(x) = [ f(x,a+da) - f(x,a-da) ] / 2,

//

// with f(x) = the plotted curve

// 'da' = error taken from the fit result

// Corr(a,a') = the correlation matrix from the fit result

// Z = requested significance 'Z sigma band'

//

// The linear method is fast (required 2*N evaluations of the curve, where N is the number of parameters),

// but may not be accurate in the presence of strong correlations (~>0.9) and at Z>2 due to linear and

// Gaussian approximations made

//

// Calculate error using sampling method and visualize as dashed red line.

//

// In this method a number of curves is calculated with variations of the parameter values, as sampled

// from a multi-variate Gaussian pdf that is constructed from the fit results covariance matrix.

// The error(x) is determined by calculating a central interval that capture N% of the variations

// for each value of x, where N% is controlled by Z (i.e. Z=1 gives N=68%). The number of sampling curves

// is chosen to be such that at least 100 curves are expected to be outside the N% interval, and is minimally

// 100 (e.g. Z=1->Ncurve=356, Z=2->Ncurve=2156)) Intervals from the sampling method can be asymmetric,

// and may perform better in the presence of strong correlations, but may take (much) longer to calculate

// Perform the same type of error visualization on the background component only.

// The VisualizeError() option can generally applied to _any_ kind of plot (components, asymmetries, efficiencies

// etc..)

model.plotOn(frame, VisualizeError(*r, 1, kFALSE), DrawOption("L"), LineWidth(2), LineColor(kRed), Components("bkg"),

LineStyle(kDashed));

// Overlay central value

model.plotOn(frame);

model.plotOn(frame, Components("bkg"), LineStyle(kDashed));

d->plotOn(frame);

frame->SetMinimum(0);

// V i s u a l i z e p a r t i a l f i t e r r o r

// ------------------------------------------------------

// Make plot frame

// Visualize partial error. For partial error visualization the covariance matrix is first reduced as follows

// ___ -1

// Vred = V22 = V11 - V12 * V22 * V21

//

// Where V11,V12,V21,V22 represent a block decomposition of the covariance matrix into observables that

// are propagated (labeled by index '1') and that are not propagated (labeled by index '2'), and V22bar

// is the Shur complement of V22, calculated as shown above

//

// (Note that Vred is _not_ a simple sub-matrix of V)

// Propagate partial error due to shape parameters (m,m2) using linear and sampling method

model.plotOn(frame2);

model.plotOn(frame2, Components("bkg"), LineStyle(kDashed));

frame2->SetMinimum(0);

// Make plot frame

// Propagate partial error due to yield parameter using linear and sampling method

model.plotOn(frame3, Components("bkg"), VisualizeError(*r, RooArgSet(s, s2), 2), FillColor(kGreen));

model.plotOn(frame3);

model.plotOn(frame3, Components("bkg"), LineStyle(kDashed));

frame3->SetMinimum(0);

// Make plot frame

// Propagate partial error due to yield parameter using linear and sampling method

model.plotOn(frame4, Components("bkg"), VisualizeError(*r, RooArgSet(fsig), 2), FillColor(kMagenta));

model.plotOn(frame4);

model.plotOn(frame4, Components("bkg"), LineStyle(kDashed));

frame4->SetMinimum(0);

c->Divide(2, 2);

c->cd(1);

gPad->SetLeftMargin(0.15);

frame->GetYaxis()->SetTitleOffset(1.4);

frame->Draw();

c->cd(2);

gPad->SetLeftMargin(0.15);

frame2->GetYaxis()->SetTitleOffset(1.6);

frame2->Draw();

c->cd(3);

gPad->SetLeftMargin(0.15);

frame3->GetYaxis()->SetTitleOffset(1.6);

frame3->Draw();

c->cd(4);

gPad->SetLeftMargin(0.15);

frame4->GetYaxis()->SetTitleOffset(1.6);

frame4->Draw();

}

RooAbsData is the common abstract base class for binned and unbinned datasets.

RooAddPdf is an efficient implementation of a sum of PDFs of the form.

RooArgList is a container object that can hold multiple RooAbsArg objects.

RooArgSet is a container object that can hold multiple RooAbsArg objects.

RooFitResult is a container class to hold the input and output of a PDF fit to a dataset.

A RooPlot is a plot frame and a container for graphics objects within that frame.

virtual void SetMinimum(Double_t minimum=-1111)

Set minimum value of Y axis.

static RooPlot * frame(const RooAbsRealLValue &var, Double_t xmin, Double_t xmax, Int_t nBins)

Create a new frame for a given variable in x.

virtual void Draw(Option_t *options=0)

Draw this plot and all of the elements it contains.

RooRealVar represents a variable that can be changed from the outside.

virtual void SetTitleOffset(Float_t offset=1)

Set distance between the axis and the axis title.

The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...

- Date
- April 2009

Definition in file rf610_visualerror.C.