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rf204_extrangefit.py File Reference

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 rf204_extrangefit
 

Detailed Description

View in nbviewer Open in SWAN Addition and convolution: extended maximum likelihood fit with alternate range definition for observed number of events.

import ROOT
# Set up component pdfs
# ---------------------------------------
# Declare observable x
x = ROOT.RooRealVar("x", "x", 0, 10)
# 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., 1.)
a1 = ROOT.RooRealVar("a1", "a1", -0.2, 0., 1.)
bkg = ROOT.RooChebychev("bkg", "Background", x, ROOT.RooArgList(a0, a1))
# Sum the signal components into a composite signal pdf
sig1frac = ROOT.RooRealVar(
"sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.)
sig = ROOT.RooAddPdf(
"sig", "Signal", ROOT.RooArgList(sig1, sig2), ROOT.RooArgList(sig1frac))
# Construct extended comps with range spec
# ------------------------------------------------------------------------------
# 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., 10000)
nbkg = ROOT.RooRealVar(
"nbkg", "number of background events in signalRange", 500, 0, 10000)
esig = ROOT.RooExtendPdf(
"esig", "extended signal pdf", sig, nsig, "signalRange")
ebkg = ROOT.RooExtendPdf(
"ebkg", "extended background pdf", bkg, nbkg, "signalRange")
# Sum extended components
# ---------------------------------------------
# Construct sum of two extended pdf (no coefficients required)
model = ROOT.RooAddPdf("model", "(g1+g2)+a", ROOT.RooArgList(ebkg, esig))
# Sample data, fit model
# -------------------------------------------
# Generate 1000 events from model so that nsig, come out to numbers <<500
# in fit
data = model.generate(ROOT.RooArgSet(x), 1000)
# Perform unbinned extended ML fit to data
r = model.fitTo(data, ROOT.RooFit.Extended(ROOT.kTRUE), ROOT.RooFit.Save())
r.Print()
Date
February 2018
Authors
Clemens Lange, Wouter Verkerke (C++ version)

Definition in file rf204_extrangefit.py.