# rf608_fitresultaspdf¶

Likelihood and minimization: representing the parabolic approximation of the fit as a multi-variate Gaussian on the parameters of the fitted pdf

Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, November 30, 2022 at 11:23 AM.

In [ ]:
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooFitResult.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "TFile.h"
#include "TStyle.h"
#include "TH2.h"
#include "TH3.h"

using namespace RooFit;


## Create model and dataset¶

Observable

In [ ]:
RooRealVar x("x", "x", -20, 20);


Model (intentional strong correlations)

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RooRealVar mean("mean", "mean of g1 and g2", 0, -1, 1);
RooRealVar sigma_g1("sigma_g1", "width of g1", 2);
RooGaussian g1("g1", "g1", x, mean, sigma_g1);

RooRealVar sigma_g2("sigma_g2", "width of g2", 4, 3.0, 5.0);
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

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


## Fit model to data¶

In [ ]:
RooFitResult *r = model.fitTo(*data, Save());


## CreateMV Gaussian pdf of fitted parameters¶

In [ ]:
RooAbsPdf *parabPdf = r->createHessePdf(RooArgSet(frac, mean, sigma_g2));


## Some execercises with the parameter pdf¶

Generate 100K points in the parameter space, sampled from the MVGaussian pdf

In [ ]:
RooDataSet *d = parabPdf->generate(RooArgSet(mean, sigma_g2, frac), 100000);


Sample a 3-D histogram of the pdf to be visualized as an error ellipsoid using the GLISO draw option

In [ ]:
TH3 *hh_3d = (TH3 *)parabPdf->createHistogram("mean,sigma_g2,frac", 25, 25, 25);
hh_3d->SetFillColor(kBlue);


Project 3D parameter pdf down to 3 permutations of two-dimensional pdfs The integrations corresponding to these projections are performed analytically by the MV Gaussian pdf

In [ ]:
RooAbsPdf *pdf_sigmag2_frac = parabPdf->createProjection(mean);
RooAbsPdf *pdf_mean_frac = parabPdf->createProjection(sigma_g2);
RooAbsPdf *pdf_mean_sigmag2 = parabPdf->createProjection(frac);


Make 2D plots of the 3 two-dimensional pdf projections

In [ ]:
TH2 *hh_sigmag2_frac = (TH2 *)pdf_sigmag2_frac->createHistogram("sigma_g2,frac", 50, 50);
TH2 *hh_mean_frac = (TH2 *)pdf_mean_frac->createHistogram("mean,frac", 50, 50);
TH2 *hh_mean_sigmag2 = (TH2 *)pdf_mean_sigmag2->createHistogram("mean,sigma_g2", 50, 50);
hh_mean_frac->SetLineColor(kBlue);
hh_sigmag2_frac->SetLineColor(kBlue);
hh_mean_sigmag2->SetLineColor(kBlue);


Draw the 'sigar'

In [ ]:
new TCanvas("rf608_fitresultaspdf_1", "rf608_fitresultaspdf_1", 600, 600);
hh_3d->Draw("iso");


Draw the 2D projections of the 3D pdf

In [ ]:
TCanvas *c2 = new TCanvas("rf608_fitresultaspdf_2", "rf608_fitresultaspdf_2", 900, 600);
c2->Divide(3, 2);
c2->cd(1);
hh_mean_sigmag2->GetZaxis()->SetTitleOffset(1.4);
hh_mean_sigmag2->Draw("surf3");
c2->cd(2);
hh_sigmag2_frac->GetZaxis()->SetTitleOffset(1.4);
hh_sigmag2_frac->Draw("surf3");
c2->cd(3);
hh_mean_frac->GetZaxis()->SetTitleOffset(1.4);
hh_mean_frac->Draw("surf3");


Draw the distributions of parameter points sampled from the pdf

In [ ]:
TH1 *tmp1 = d->createHistogram("mean,sigma_g2", Binning(50), Binning(50));
TH1 *tmp2 = d->createHistogram("sigma_g2,frac", Binning(50), Binning(50));
TH1 *tmp3 = d->createHistogram("mean,frac", Binning(50), Binning(50));

c2->cd(4);
tmp1->GetZaxis()->SetTitleOffset(1.4);
tmp1->Draw("lego3");
c2->cd(5);

gROOT->GetListOfCanvases()->Draw()