Rf 8 0 1_Mcstudy¶

Validation and MC studies: toy Monte Carlo study that perform cycles of event generation and fitting

Author: Clemens Lange, Wouter Verkerke (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, January 19, 2022 at 10:37 AM.

In [ ]:
import ROOT

Create model¶

Declare observable x

In [ ]:
x = ROOT.RooRealVar("x", "x", 0, 10)
x.setBins(40)

Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters

In [ ]:
mean = ROOT.RooRealVar("mean", "mean of gaussians", 5, 0, 10)
sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)
sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)

sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)

Build Chebychev polynomial pdf

In [ ]:
a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0.0, 1.0)
a1 = ROOT.RooRealVar("a1", "a1", -0.2, -1, 1.0)
bkg = ROOT.RooChebychev("bkg", "Background", x, [a0, a1])

Sum the signal components into a composite signal pdf

In [ ]:
sig1frac = ROOT.RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8, 0.0, 1.0)
sig = ROOT.RooAddPdf("sig", "Signal", [sig1, sig2], [sig1frac])

Sum the composite signal and background

In [ ]:
nbkg = ROOT.RooRealVar("nbkg", "number of background events, ", 150, 0, 1000)
nsig = ROOT.RooRealVar("nsig", "number of signal events", 150, 0, 1000)
model = ROOT.RooAddPdf("model", "g1+g2+a", [bkg, sig], [nbkg, nsig])

Create manager¶

Instantiate ROOT.RooMCStudy manager on model with x as observable and given choice of fit options

The Silence() option kills all messages below the PROGRESS level, only a single message per sample executed, any error message that occur during fitting

The Extended() option has two effects: 1) The extended ML term is included in the likelihood and 2) A poisson fluctuation is introduced on the number of generated events

The FitOptions() given here are passed to the fitting stage of each toy experiment. If Save() is specified, fit result of each experiment is saved by the manager

A Binned() option is added in self example to bin the data between generation and fitting to speed up the study at the expemse of some precision

In [ ]:
mcstudy = ROOT.RooMCStudy(
model,
{x},
Binned=True,
Silence=True,
Extended=True,
FitOptions=dict(Save=True, PrintEvalErrors=0),
)

Generate and fit events¶

Generate and fit 1000 samples of Poisson(nExpected) events

In [ ]:
mcstudy.generateAndFit(1000)

Explore results of study¶

Make plots of the distributions of mean, error on mean and the pull of mean

In [ ]:
frame1 = mcstudy.plotParam(mean, Bins=40)
frame2 = mcstudy.plotError(mean, Bins=40)
frame3 = mcstudy.plotPull(mean, Bins=40, FitGauss=True)

Plot distribution of minimized likelihood

In [ ]:
frame4 = mcstudy.plotNLL(Bins=40)

Make some histograms from the parameter dataset

In [ ]:
hh_cor_a0_s1f = ROOT.RooAbsData.createHistogram(mcstudy.fitParDataSet(), "hh", a1, YVar=sig1frac)
hh_cor_a0_a1 = ROOT.RooAbsData.createHistogram(mcstudy.fitParDataSet(), "hh", a0, YVar=a1)

Access some of the saved fit results from individual toys

In [ ]:
corrHist000 = mcstudy.fitResult(0).correlationHist("c000")
corrHist127 = mcstudy.fitResult(127).correlationHist("c127")
corrHist953 = mcstudy.fitResult(953).correlationHist("c953")

Draw all plots on a canvas

In [ ]:
ROOT.gStyle.SetPalette(1)
ROOT.gStyle.SetOptStat(0)
c = ROOT.TCanvas("rf801_mcstudy", "rf801_mcstudy", 900, 900)
c.Divide(3, 3)
c.cd(1)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.Draw()
c.cd(2)
frame2.GetYaxis().SetTitleOffset(1.4)
frame2.Draw()
c.cd(3)
frame3.GetYaxis().SetTitleOffset(1.4)
frame3.Draw()
c.cd(4)
frame4.GetYaxis().SetTitleOffset(1.4)
frame4.Draw()
c.cd(5)
hh_cor_a0_s1f.GetYaxis().SetTitleOffset(1.4)
hh_cor_a0_s1f.Draw("box")
c.cd(6)
hh_cor_a0_a1.GetYaxis().SetTitleOffset(1.4)
hh_cor_a0_a1.Draw("box")
c.cd(7)
corrHist000.GetYaxis().SetTitleOffset(1.4)
corrHist000.Draw("colz")
c.cd(8)
corrHist127.GetYaxis().SetTitleOffset(1.4)
corrHist127.Draw("colz")
c.cd(9)
corrHist953.GetYaxis().SetTitleOffset(1.4)
corrHist953.Draw("colz")

c.SaveAs("rf801_mcstudy.png")

Make ROOT.RooMCStudy object available on command line after macro finishes

In [ ]: