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rf701_efficiencyfit.py File Reference

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 rf701_efficiencyfit
 

Detailed Description

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Special p.d.f.'s: unbinned maximum likelihood fit of an efficiency eff(x) function to a dataset D(x,cut), cut is a category encoding a selection, which the efficiency as function of x should be described by eff(x)

import ROOT
# Construct efficiency function e(x)
# -------------------------------------------------------------------
# Declare variables x,mean, with associated name, title, value and allowed
# range
x = ROOT.RooRealVar("x", "x", -10, 10)
# Efficiency function eff(x;a,b)
a = ROOT.RooRealVar("a", "a", 0.4, 0, 1)
b = ROOT.RooRealVar("b", "b", 5)
c = ROOT.RooRealVar("c", "c", -1, -10, 10)
effFunc = ROOT.RooFormulaVar(
"effFunc", "(1-a)+a*cos((x-c)/b)", ROOT.RooArgList(a, b, c, x))
# Construct conditional efficiency pdf E(cut|x)
# ------------------------------------------------------------------------------------------
# Acceptance state cut (1 or 0)
cut = ROOT.RooCategory("cut", "cutr")
cut.defineType("accept", 1)
cut.defineType("reject", 0)
# Construct efficiency p.d.f eff(cut|x)
effPdf = ROOT.RooEfficiency("effPdf", "effPdf", effFunc, cut, "accept")
# Generate data (x, cut) from a toy model
# -----------------------------------------------------------------------------
# Construct global shape p.d.f shape(x) and product model(x,cut) = eff(cut|x)*shape(x)
# (These are _only_ needed to generate some toy MC here to be used later)
shapePdf = ROOT.RooPolynomial(
"shapePdf", "shapePdf", x, ROOT.RooArgList(ROOT.RooFit.RooConst(-0.095)))
model = ROOT.RooProdPdf(
"model",
"model",
ROOT.RooArgSet(shapePdf),
ROOT.RooFit.Conditional(
ROOT.RooArgSet(effPdf),
ROOT.RooArgSet(cut)))
# Generate some toy data from model
data = model.generate(ROOT.RooArgSet(x, cut), 10000)
# Fit conditional efficiency pdf to data
# --------------------------------------------------------------------------
# Fit conditional efficiency p.d.f to data
effPdf.fitTo(data, ROOT.RooFit.ConditionalObservables(ROOT.RooArgSet(x)))
# Plot fitted, data efficiency
# --------------------------------------------------------
# Plot distribution of all events and accepted fraction of events on frame
frame1 = x.frame(ROOT.RooFit.Bins(
20), ROOT.RooFit.Title("Data (all, accepted)"))
data.plotOn(frame1)
data.plotOn(
frame1,
ROOT.RooFit.Cut("cut==cut::accept"),
ROOT.RooFit.MarkerColor(
ROOT.kRed),
ROOT.RooFit.LineColor(
ROOT.kRed))
# Plot accept/reject efficiency on data overlay fitted efficiency curve
frame2 = x.frame(ROOT.RooFit.Bins(
20), ROOT.RooFit.Title("Fitted efficiency"))
data.plotOn(frame2, ROOT.RooFit.Efficiency(cut)) # needs ROOT version >= 5.21
effFunc.plotOn(frame2, ROOT.RooFit.LineColor(ROOT.kRed))
# Draw all frames on a canvas
ca = ROOT.TCanvas("rf701_efficiency", "rf701_efficiency", 800, 400)
ca.Divide(2)
ca.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
frame1.GetYaxis().SetTitleOffset(1.6)
frame1.Draw()
ca.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
frame2.GetYaxis().SetTitleOffset(1.4)
frame2.Draw()
ca.SaveAs("rf701_efficiencyfit.png")
Date
February 2018
Authors
Clemens Lange, Wouter Verkerke (C++ version)

Definition in file rf701_efficiencyfit.py.