# rf605_profilell¶

'LIKELIHOOD AND MINIMIZATION' RooFit tutorial macro #605

Working with the profile likelihood estimator

Author: Clemens Lange, Wouter Verkerke (C version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Sunday, November 27, 2022 at 11:08 AM.

In [1]:
import ROOT
Welcome to JupyROOT 6.27/01

## Create model and dataset¶

Observable

In [2]:
x = ROOT.RooRealVar("x", "x", -20, 20)

Model (intentional strong correlations)

In [3]:
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])
[#0] WARNING:InputArguments -- The parameter 'sigma_g1' with range [-1e+30, 1e+30] of the RooGaussian 'g1' exceeds the safe range of (0, inf). Advise to limit its range.

Generate 1000 events

In [4]:
data = model.generate({x}, 1000)

## Construct plain likelihood¶

Construct unbinned likelihood

In [5]:
nll = model.createNLL(data, NumCPU=2)

Minimize likelihood w.r.t all parameters before making plots

In [6]:
Out[6]:
0
**********
**    1 **SET PRINT           1
**********
**********
**********
PARAMETER DEFINITIONS:
NO.   NAME         VALUE      STEP SIZE      LIMITS
1 frac         5.00000e-01  1.00000e-01    0.00000e+00  1.00000e+00
2 mean         0.00000e+00  2.00000e+00   -1.00000e+01  1.00000e+01
3 sigma_g2     4.00000e+00  3.00000e-01    3.00000e+00  6.00000e+00
**********
**    3 **SET ERR         0.5
**********
**********
**    4 **SET PRINT           1
**********
**********
**    5 **SET STR           1
**********
NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.
START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=2660.22 FROM MIGRAD    STATUS=INITIATE       10 CALLS          11 TOTAL
EDM= unknown      STRATEGY= 1      NO ERROR MATRIX
EXT PARAMETER               CURRENT GUESS       STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  frac         5.00000e-01   1.00000e-01   2.01358e-01  -5.61980e+00
2  mean         0.00000e+00   2.00000e+00   2.01358e-01  -7.16779e+00
3  sigma_g2     4.00000e+00   3.00000e-01   2.14402e-01   7.28535e+00
ERR DEF= 0.5
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=2659.74 FROM MIGRAD    STATUS=CONVERGED      67 CALLS          68 TOTAL
EDM=5.19798e-06    STRATEGY= 1      ERROR MATRIX ACCURATE
EXT PARAMETER                                   STEP         FIRST
NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
1  frac         6.23972e-01   1.64510e-01   5.33134e-03   6.83204e-03
2  mean         4.57491e-03   1.09369e-01   3.87767e-04  -1.84350e-01
3  sigma_g2     4.11576e+00   4.07375e-01   4.33560e-03  -6.97269e-03
ERR DEF= 0.5
EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  3    ERR DEF=0.5
2.817e-02 -1.610e-03  6.258e-02
-1.610e-03  1.196e-02 -4.302e-03
6.258e-02 -4.302e-03  1.705e-01
PARAMETER  CORRELATION COEFFICIENTS
NO.  GLOBAL      1      2      3
1  0.90293   1.000 -0.088  0.903
2  0.09533  -0.088  1.000 -0.095
3  0.90308   0.903 -0.095  1.000

Plot likelihood scan frac

In [7]:
frame1 = frac.frame(Bins=10, Range=(0.01, 0.95), Title="LL and profileLL in frac")
nll.plotOn(frame1, ShiftToZero=True)
Out[7]:
<cppyy.gbl.RooPlot object at 0x96674f0>
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.

Plot likelihood scan in sigma_g2

In [8]:
frame2 = sigma_g2.frame(Bins=10, Range=(3.3, 5.0), Title="LL and profileLL in sigma_g2")
nll.plotOn(frame2, ShiftToZero=True)
Out[8]:
<cppyy.gbl.RooPlot object at 0x96cd300>
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.

## 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

In [9]:
pll_frac = nll.createProfile({frac})

Plot the profile likelihood in frac

In [10]:
pll_frac.plotOn(frame1, LineColor="r")
Out[10]:
<cppyy.gbl.RooPlot object at 0x96674f0>
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[frac]) Creating instance of MINUIT
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[frac]) determining minimum likelihood for current configurations w.r.t all observable
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[frac]) minimum found at (frac=0.623915)
..................................................................................

Adjust frame maximum for visual clarity

In [11]:
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

In [12]:
pll_sigmag2 = nll.createProfile({sigma_g2})

Plot the profile likelihood in sigma_g2

In [13]:
pll_sigmag2.plotOn(frame2, LineColor="r")
Out[13]:
<cppyy.gbl.RooPlot object at 0x96cd300>
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[sigma_g2]) Creating instance of MINUIT
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[sigma_g2]) determining minimum likelihood for current configurations w.r.t all observable
[#1] INFO:Eval -- RooAbsTestStatistic::initMPMode: started 2 remote server process.
[#1] INFO:Minimization -- RooProfileLL::evaluate(nll_model_modelData_Profile[sigma_g2]) minimum found at (sigma_g2=4.11588)
....................................................................................

Adjust frame maximum for visual clarity

In [14]:
frame2.SetMinimum(0)
frame2.SetMaximum(3)

Make canvas and draw ROOT.RooPlots

In [15]:
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)