rf801_mcstudy.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## Validation and MC studies: toy Monte Carlo study that perform cycles of event generation and fitting
##
## \macro_code
##
## \date February 2018
## \authors Clemens Lange, Wouter Verkerke (C++ version)
 
import ROOT
 
 
# Create model
# -----------------------
 
# Declare observable x
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
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
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
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
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
 
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
mcstudy.generateAndFit(1000)
 
# Explore results of study
# ------------------------------------------------
 
# Make plots of the distributions of mean, error on mean and the pull of
# mean
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
frame4 = mcstudy.plotNLL(Bins=40)
 
# Make some histograms from the parameter dataset
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
corrHist000 = mcstudy.fitResult(0).correlationHist("c000")
corrHist127 = mcstudy.fitResult(127).correlationHist("c127")
corrHist953 = mcstudy.fitResult(953).correlationHist("c953")
 
# Draw all plots on a canvas
ROOT.gStyle.SetPalette(1)
ROOT.gStyle.SetOptStat(0)
c = ROOT.TCanvas("rf801_mcstudy", "rf801_mcstudy", 900, 900)
c.Divide(3, 3)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.Draw()
c.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
frame2.GetYaxis().SetTitleOffset(1.4)
frame2.Draw()
c.cd(3)
ROOT.gPad.SetLeftMargin(0.15)
frame3.GetYaxis().SetTitleOffset(1.4)
frame3.Draw()
c.cd(4)
ROOT.gPad.SetLeftMargin(0.15)
frame4.GetYaxis().SetTitleOffset(1.4)
frame4.Draw()
c.cd(5)
ROOT.gPad.SetLeftMargin(0.15)
hh_cor_a0_s1f.GetYaxis().SetTitleOffset(1.4)
hh_cor_a0_s1f.Draw("box")
c.cd(6)
ROOT.gPad.SetLeftMargin(0.15)
hh_cor_a0_a1.GetYaxis().SetTitleOffset(1.4)
hh_cor_a0_a1.Draw("box")
c.cd(7)
ROOT.gPad.SetLeftMargin(0.15)
corrHist000.GetYaxis().SetTitleOffset(1.4)
corrHist000.Draw("colz")
c.cd(8)
ROOT.gPad.SetLeftMargin(0.15)
corrHist127.GetYaxis().SetTitleOffset(1.4)
corrHist127.Draw("colz")
c.cd(9)
ROOT.gPad.SetLeftMargin(0.15)
corrHist953.GetYaxis().SetTitleOffset(1.4)
corrHist953.Draw("colz")
 
c.SaveAs("rf801_mcstudy.png")
 
# Make ROOT.RooMCStudy object available on command line after
# macro finishes
ROOT.gDirectory.Add(mcstudy)