Rf 2 1 2_Plotting In Ranges_Blinding¶

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().

Author: Harshal Shende, Stephan Hageboeck (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, January 17, 2022 at 09:57 AM.

In [ ]:
import ROOT

Make a fit model

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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)

In [ ]:
x.setRange("full", 1, 30)
x.setRange("left", 1, 10)
x.setRange("right", 20, 30)

Generate toy data, and cut out the blinded region.

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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.¶

In [ ]:
tau.setVal(-2.0)
exp.fitTo(blindedData)

Here we will plot the results

In [ ]:
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.¶

In [ ]:
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

In [ ]:
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.¶

In [ ]:
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

In [ ]:
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")

Draw all canvases

In [ ]:
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()