ROOT   Reference Guide
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
12 import ROOT
13
14 # Set up component pdfs
15 # ---------------------------------------
16
17 # Declare observable x
18 x = 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
22 mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)
23 sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)
24 sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)
25
26 sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
27 sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
28
29 # Build Chebychev polynomial pdf
30 a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0., 1.)
31 a1 = ROOT.RooRealVar("a1", "a1", -0.2, 0., 1.)
32 bkg = ROOT.RooChebychev("bkg", "Background", x, ROOT.RooArgList(a0, a1))
33
34 # Sum the signal components into a composite signal pdf
35 sig1frac = ROOT.RooRealVar(
36  "sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.)
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
44 x.setRange("signalRange", 4, 6)
45
46 # Associated nsig/nbkg as expected number of events with sig/bkg
47 # _in_the_range_ "signalRange"
48 nsig = ROOT.RooRealVar(
49  "nsig", "number of signal events in signalRange", 500, 0., 10000)
50 nbkg = ROOT.RooRealVar(
51  "nbkg", "number of background events in signalRange", 500, 0, 10000)
52 esig = ROOT.RooExtendPdf(
53  "esig", "extended signal pdf", sig, nsig, "signalRange")
54 ebkg = 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)
61 model = 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
68 data = model.generate(ROOT.RooArgSet(x), 1000)
69
70 # Perform unbinned extended ML fit to data
71 r = model.fitTo(data, ROOT.RooFit.Extended(ROOT.kTRUE), ROOT.RooFit.Save())
72 r.Print()