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rf204_extrangefit.py
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1## \file
2## \ingroup tutorial_roofit
3## \notebook -nodraw
4## Addition and convolution: extended maximum likelihood fit with alternate range definition
5## for observed number of events.
6##
7## \macro_code
8##
9## \date February 2018
10## \authors Clemens Lange, Wouter Verkerke (C++ version)
11
12import ROOT
13
14# Set up component pdfs
15# ---------------------------------------
16
17# Declare observable x
18x = ROOT.RooRealVar("x", "x", 0, 10)
19
20# Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and
21# their parameters
22mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)
23sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)
24sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)
25
26sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
27sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
28
29# Build Chebychev polynomial pdf
30a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0., 1.)
31a1 = ROOT.RooRealVar("a1", "a1", -0.2, 0., 1.)
32bkg = ROOT.RooChebychev("bkg", "Background", x, ROOT.RooArgList(a0, a1))
33
34# Sum the signal components into a composite signal pdf
35sig1frac = ROOT.RooRealVar(
36 "sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.)
37sig = ROOT.RooAddPdf(
38 "sig", "Signal", ROOT.RooArgList(sig1, sig2), ROOT.RooArgList(sig1frac))
39
40# Construct extended comps with range spec
41# ------------------------------------------------------------------------------
42
43# Define signal range in which events counts are to be defined
44x.setRange("signalRange", 4, 6)
45
46# Associated nsig/nbkg as expected number of events with sig/bkg
47# _in_the_range_ "signalRange"
48nsig = ROOT.RooRealVar(
49 "nsig", "number of signal events in signalRange", 500, 0., 10000)
50nbkg = ROOT.RooRealVar(
51 "nbkg", "number of background events in signalRange", 500, 0, 10000)
52esig = ROOT.RooExtendPdf(
53 "esig", "extended signal pdf", sig, nsig, "signalRange")
54ebkg = ROOT.RooExtendPdf(
55 "ebkg", "extended background pdf", bkg, nbkg, "signalRange")
56
57# Sum extended components
58# ---------------------------------------------
59
60# Construct sum of two extended pdf (no coefficients required)
61model = ROOT.RooAddPdf("model", "(g1+g2)+a", ROOT.RooArgList(ebkg, esig))
62
63# Sample data, fit model
64# -------------------------------------------
65
66# Generate 1000 events from model so that nsig, come out to numbers <<500
67# in fit
68data = model.generate(ROOT.RooArgSet(x), 1000)
69
70# Perform unbinned extended ML fit to data
71r = model.fitTo(data, ROOT.RooFit.Extended(ROOT.kTRUE), ROOT.RooFit.Save())
72r.Print()