rf212_plottingInRanges_blinding.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## Plot a PDF in disjunct ranges, and get normalisation right.
##
## Usually, when comparing a fit to data, one should first plot the data, and then the PDF.
## In this case, the PDF is automatically normalised to match the number of data events in the plot.
## However, when plotting only a sub-range, when e.g. a signal region has to be blinded,
## one has to exclude the blinded region from the computation of the normalisation.
##
## In this tutorial, we show how to explicitly choose the normalisation when plotting using `NormRange()`.
##
## \macro_code
##
## \date June 2021
## \author Harshal Shende, Stephan Hageboeck (C++ version)
 
import ROOT
 
# Make a fit model
x = ROOT.RooRealVar("x", "The observable", 1, 30)
tau = ROOT.RooRealVar("tau", "The exponent", -0.1337, -10.0, -0.1)
exp = ROOT.RooExponential("exp", "A falling exponential function", x, tau)
 
# Define the sidebands (e.g. background regions)
x.setRange("full", 1, 30)
x.setRange("left", 1, 10)
x.setRange("right", 20, 30)
 
# Generate toy data, and cut out the blinded region.
data = exp.generate(x, 1000)
blindedData = data.reduce(CutRange="left,right")
 
# Kick tau a bit, and run an unbinned fit where the blinded data are missing.
# ----------------------------------------------------------------------------------------------------------
tau.setVal(-2.0)
exp.fitTo(blindedData)
 
 
# Here we will plot the results
canvas = ROOT.TCanvas("canvas", "canvas", 800, 600)
canvas.Divide(2, 1)
 
 
# Wrong:
# Plotting each slice on its own normalises the PDF over its plotting range. For the full curve, that means
# that the blinded region where data is missing is included in the normalisation calculation. The PDF therefore
# comes out too low, and doesn't match up with the slices in the side bands, which are normalised to "their" data.
# ----------------------------------------------------------------------------------------------------------
 
print("Now plotting with unique normalisation for each slice.\n")
canvas.cd(1)
plotFrame = x.frame(Title="Wrong: Each slice normalised over its plotting range")
 
# Plot only the blinded data, and then plot the PDF over the full range as well as both sidebands
blindedData.plotOn(plotFrame)
exp.plotOn(plotFrame, LineColor="r", Range="full")
exp.plotOn(plotFrame, LineColor="b", Range="left")
exp.plotOn(plotFrame, LineColor="g", Range="right")
 
plotFrame.Draw()
 
# Right:
# Make the same plot, but normalise each piece with respect to the regions "left" AND "right". This requires setting
# a "NormRange", which tells RooFit over which range the PDF has to be integrated to normalise.
# This is means that the normalisation of the blue and green curves is slightly different from the left plot,
# because they get a common scale factor.
# ----------------------------------------------------------------------------------------------------------
 
print("\n\nNow plotting with correct norm ranges:\n")
canvas.cd(2)
plotFrameWithNormRange = x.frame(Title="Right: All slices have common normalisation")
 
# Plot only the blinded data, and then plot the PDF over the full range as well as both sidebands
blindedData.plotOn(plotFrameWithNormRange)
exp.plotOn(plotFrameWithNormRange, LineColor="b", Range="left", NormRange="left,right")
exp.plotOn(plotFrameWithNormRange, LineColor="g", Range="right", NormRange="left,right")
exp.plotOn(plotFrameWithNormRange, LineColor="r", Range="full", NormRange="left,right", LineStyle=10)
 
plotFrameWithNormRange.Draw()
 
canvas.Draw()
 
canvas.SaveAs("rf212_plottingInRanges_blinding.png")