rf606_nllerrorhandling.py

## \ingroup tutorial_roofit_main

## \notebook

## 'LIKELIHOOD AND MINIMIZATION' RooFit tutorial macro #606

##

## Understanding and customizing error handling in likelihood evaluations

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

## \authors Clemens Lange, Wouter Verkerke (C version)

import ROOT

# Create model and dataset

# ----------------------------------------------

# Observable

m = ROOT.RooRealVar("m", "m", 5.20, 5.30)

# Parameters

m0 = ROOT.RooRealVar("m0", "m0", 5.291, 5.20, 5.30)

k = ROOT.RooRealVar("k", "k", -30, -50, -10)

# Pdf

argus = ROOT.RooArgusBG("argus", "argus", m, m0, k)

# Sample 1000 events in m from argus

data = argus.generate({m}, 1000)

# Plot model and data

# --------------------------------------

frame1 = m.frame(Bins=40, Title="Argus model and data")

data.plotOn(frame1)

argus.plotOn(frame1)

# Fit model to data

# ---------------------------------

# The ARGUS background shape has a sharp kinematic cutoff at m=m0

# and is prone to evaluation errors if the cutoff parameter m0

# is floated: when the pdf cutoff value is lower than that in data

# events with m>m0 will have zero probability

# Perform unbinned ML fit. Print detailed error messages for up to

# 10 events per likelihood evaluation. The default error handling strategy

# is to return a very high value of the likelihood to MINUIT if errors occur,

# which will force MINUIT to retreat from the problematic area

argus.fitTo(data, PrintEvalErrors=10)

# Perform another fit. In self configuration only the number of errors per

# likelihood evaluation is shown, it is greater than zero. The

# EvalErrorWall(kFALSE) arguments disables the default error handling strategy

# and will cause the actual (problematic) value of the likelihood to be passed

# to MINUIT.

#

# NB: Use of self option is NOT recommended as default strategt as broken -log(L) values

# can often be lower than 'good' ones because offending events are removed.

# ROOT.This may effectively create a False minimum in problem areas. ROOT.This is clearly

# illustrated in the second plot

m0.setError(0.1)

argus.fitTo(data, PrintEvalErrors=0, EvalErrorWall=False)

# Plot likelihood as function of m0

# ------------------------------------------------------------------

# Construct likelihood function of model and data

nll = argus.createNLL(data)

# Plot likelihood in m0 in range that includes problematic values

# In self configuration no messages are printed for likelihood evaluation errors,

# but if an likelihood value evaluates with error, corresponding value

# on the curve will be set to the value given in EvalErrorValue().

frame2 = m0.frame(Range=(5.288, 5.293), Title="-log(L) scan vs m0, regions masked")

nll.plotOn(frame2, ShiftToZero=True, PrintEvalErrors=-1, EvalErrorValue=(nll.getVal() + 10), LineColor="r")

frame2.SetMaximum(15)

frame2.SetMinimum(0)

c = ROOT.TCanvas("rf606_nllerrorhandling", "rf606_nllerrorhandling", 1200, 400)

c.Divide(2)

c.cd(1)

ROOT.gPad.SetLeftMargin(0.15)

frame1.GetYaxis().SetTitleOffset(1.4)

frame1.Draw()

c.cd(2)

ROOT.gPad.SetLeftMargin(0.15)

frame2.GetYaxis().SetTitleOffset(1.4)

frame2.Draw()

c.SaveAs("rf606_nllerrorhandling.png")