doc/v628/rf204a__extendedLikelihood_8py.html

import ROOT


# Setup component pdfs

# ---------------------


# Declare observable x

x = ROOT.RooRealVar("x", "x", 0, 11)


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

mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)

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, 0.0, 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)


# Extend the pdfs

# -----------------------------


# Define signal range in which events counts are to be defined

x.setRange("signalRange", 4, 6)


# Associated nsig/nbkg as expected number of events with sig/bkg _in_the_range_ "signalRange"

nsig = ROOT.RooRealVar("nsig", "number of signal events in signalRange", 500, 0.0, 10000)

nbkg = ROOT.RooRealVar("nbkg", "number of background events in signalRange", 500, 0, 10000)


# Use AddPdf to extend the model. Giving as many coefficients as pdfs switches on extension.

model = ROOT.RooAddPdf("model", "(g1+g2)+a", [bkg, sig], [nbkg, nsig])


# Sample data, fit model

# -------------------------------------------


# Generate 1000 events from model so that nsig,nbkg come out to numbers <<500 in fit

data = model.generate(x, 1000)


canv = ROOT.TCanvas("Canvas", "Canvas", 1500, 600)

canv.Divide(3, 1)


# Fit full range

#  -------------------------------------------


# Perform unbinned ML fit to data, full range


# IMPORTANT:

# The model needs to be copied when fitting with different ranges because

# the interpretation of the coefficients is tied to the fit range

# that's used in the first fit

canv.cd(1)


model1 = ROOT.RooAddPdf(model)

r = model1.fitTo(data, Save=True, PrintLevel=-1)

r.Print()


frame = x.frame(Title="Full range fitted")

data.plotOn(frame)

model1.plotOn(frame, VisualizeError=r)

model1.plotOn(frame)

model1.paramOn(frame)

frame.Draw()


# Fit in two regions

# -------------------------------------------


canv.cd(2)

x.setRange("left", 0.0, 4.0)

x.setRange("right", 6.0, 10.0)


model2 = ROOT.RooAddPdf(model)

r2 = model2.fitTo(data, Range="left,right", Save=True, PrintLevel=-1)

r2.Print()


frame2 = x.frame(Title="Fit in left/right sideband")

data.plotOn(frame2)

model2.plotOn(frame2, VisualizeError=r2)

model2.plotOn(frame2)

model2.paramOn(frame2)

frame2.Draw()


# Fit in one region

# -------------------------------------------

# Note how restricting the region to only the left tail increases

# the fit uncertainty


canv.cd(3)

x.setRange("leftToMiddle", 0.0, 5.0)


model3 = ROOT.RooAddPdf(model)

r3 = model3.fitTo(data, Range="leftToMiddle", Save=True, PrintLevel=-1)

r3.Print()


frame3 = x.frame(Title="Fit from left to middle")

data.plotOn(frame3)

model3.plotOn(frame3, VisualizeError=r3)

model3.plotOn(frame3)

model3.paramOn(frame3)

frame3.Draw()


canv.Draw()


canv.SaveAs("rf204a_extendedLikelihood.png")