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rf605_profilell.py File Reference

## Detailed Description

'LIKELIHOOD AND MINIMIZATION' RooFit tutorial macro #605

Working with the profile likelihood estimator

import ROOT
# Create model and dataset
# -----------------------------------------------
# Observable
x = ROOT.RooRealVar("x", "x", -20, 20)
# Model (intentional strong correlations)
mean = ROOT.RooRealVar("mean", "mean of g1 and g2", 0, -10, 10)
sigma_g1 = ROOT.RooRealVar("sigma_g1", "width of g1", 3)
g1 = ROOT.RooGaussian("g1", "g1", x, mean, sigma_g1)
sigma_g2 = ROOT.RooRealVar("sigma_g2", "width of g2", 4, 3.0, 6.0)
g2 = ROOT.RooGaussian("g2", "g2", x, mean, sigma_g2)
frac = ROOT.RooRealVar("frac", "frac", 0.5, 0.0, 1.0)
model = ROOT.RooAddPdf("model", "model", [g1, g2], [frac])
# Generate 1000 events
data = model.generate({x}, 1000)
# Construct plain likelihood
# ---------------------------------------------------
# Construct unbinned likelihood
nll = model.createNLL(data, NumCPU=2)
# Minimize likelihood w.r.t all parameters before making plots
# Plot likelihood scan frac
frame1 = frac.frame(Bins=10, Range=(0.01, 0.95), Title="LL and profileLL in frac")
nll.plotOn(frame1, ShiftToZero=True)
# Plot likelihood scan in sigma_g2
frame2 = sigma_g2.frame(Bins=10, Range=(3.3, 5.0), Title="LL and profileLL in sigma_g2")
nll.plotOn(frame2, ShiftToZero=True)
# Construct profile likelihood in frac
# -----------------------------------------------------------------------
# The profile likelihood estimator on nll for frac will minimize nll w.r.t
# all floating parameters except frac for each evaluation
pll_frac = nll.createProfile({frac})
# Plot the profile likelihood in frac
pll_frac.plotOn(frame1, LineColor="r")
# Adjust frame maximum for visual clarity
frame1.SetMinimum(0)
frame1.SetMaximum(3)
# Construct profile likelihood in sigma_g2
# -------------------------------------------------------------------------------
# The profile likelihood estimator on nll for sigma_g2 will minimize nll
# w.r.t all floating parameters except sigma_g2 for each evaluation
pll_sigmag2 = nll.createProfile({sigma_g2})
# Plot the profile likelihood in sigma_g2
pll_sigmag2.plotOn(frame2, LineColor="r")
# Adjust frame maximum for visual clarity
frame2.SetMinimum(0)
frame2.SetMaximum(3)
# Make canvas and draw ROOT.RooPlots
c = ROOT.TCanvas("rf605_profilell", "rf605_profilell", 800, 400)
c.Divide(2)
c.cd(1)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.Draw()
c.cd(2)
frame2.GetYaxis().SetTitleOffset(1.4)
frame2.Draw()
c.SaveAs("rf605_profilell.png")
[#0] WARNING:InputArguments -- The parameter 'sigma_g1' with range [-inf, inf] of the RooGaussian 'g1' exceeds the safe range of (0, inf). Advise to limit its range.
[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Fitting -- using CPU computation library compiled with -mavx2
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level
Minuit2Minimizer: Minimize with max-calls 1500 convergence for edm < 1 strategy 1
Minuit2Minimizer : Valid minimum - status = 0
FVAL = 2659.73712858695399
Edm = 0.000190395763129910388
Nfcn = 60
frac = 0.62118 +/- 0.165788 (limited)
mean = 0.00442366 +/- 0.109372 (limited)
sigma_g2 = 4.10789 +/- 0.405468 (limited)
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[frac]) Creating instance of MINUIT
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[frac]) determining minimum likelihood for current configurations w.r.t all observable
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[frac]) minimum found at (frac=0.62104)
..................................................................................
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[sigma_g2]) Creating instance of MINUIT
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[sigma_g2]) determining minimum likelihood for current configurations w.r.t all observable
[#1] INFO:Minimization -- RooProfileLL::evaluate(RooEvaluatorWrapper_Profile[sigma_g2]) minimum found at (sigma_g2=4.11258)
....................................................................................
Date
February 2018

Definition in file rf605_profilell.py.