Limited Parameter Error

Roofit and RooStats
1

Hi guys,

I noticed that when I use fitTo() function and one of my parameter reaches to limit, its error is different from the sqrt of the covariance matrix.

My results are:

COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-562.676 FROM HESSE STATUS=OK 10 CALLS 108 TOTAL
EDM=3.05314e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 N1 2.06786e-05 7.74030e-01 1.83527e-04 -1.57051e+00
WARNING - - ABOVE PARAMETER IS AT LIMIT.
2 N2 1.00766e+02 1.00765e+01 3.24322e-05 1.00938e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 2 ERR DEF=0.5
6.404e-05 -3.080e-05
-3.080e-05 1.015e+02

And as you can see, the error of the limited parameter N1 (2.06786e-05) is different from the sqrt of 6.404e-05.

I would like to know how the new error is calculated. Is the covariance matrix even relevant in this case?

Any help would be appreciated!

2

@moneta could you please take a look or maybe suggest who can help here? Thank you!

3

Thank you. This problem is still relevant.

4

Hi,
Can you please post the full log coming out of Minuit? I can suggest you also to use Minuit2 as possible alternative.

Lorenzo

5

What advantage does Minuit2 over Minuit (for this case)?
Also, here is the full log:

Processing RooFitBDT.cc…

e[1mRooFit v3.60 – Developed by Wouter Verkerke and David Kirkbye[0m
Copyright © 2000-2013 NIKHEF, University of California & Stanford University
All rights reserved, please read http://roofit.sourceforge.net/license.txt

value2:0.366904

lowestBin2:0.366904

lowestBin3:0.00285088
[#1] INFO:DataHandling – RooDataHist::adjustBinning(hist_data1): fit range of variable varMLP1 expanded to nearest bin boundaries: [0,1] --> [0,1]
[#1] INFO:DataHandling – RooDataHist::adjustBinning(hist_signal): fit range of variable varMLP1 expanded to nearest bin boundaries: [0,1] --> [0,1]
[#1] INFO:DataHandling – RooDataHist::adjustBinning(hist_bg): fit range of variable varMLP1 expanded to nearest bin boundaries: [0,1] --> [0,1]
[#1] INFO:Minization – RooMinimizer::optimizeConst: activating const optimization
[#1] INFO:Minization – The following expressions have been identified as constant and will be precalculated and cached: (pdf_signal,pdf_bg)

** 1 **SET PRINT 1

** 2 **SET NOGRAD

PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 N1 5.00000e+02 1.00000e+02 0.00000e+00 1.00000e+03
2 N2 0.00000e+00 2.00000e+02 -1.00000e+03 1.00000e+03

** 3 **SET ERR 0.5

** 4 **SET PRINT 1

** 5 **SET STR 1

NOW USING STRATEGY 1: TRY TO BALANCE SPEED AGAINST RELIABILITY

** 6 **MIGRAD 1000 1

FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION. STRATEGY 1. CONVERGENCE WHEN EDM .LT. 1.00e-03
FCN=12.7399 FROM MIGRAD STATUS=INITIATE 8 CALLS 9 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 N1 5.00000e+02 1.00000e+02 2.01358e-01 4.03870e+02
2 N2 0.00000e+00 2.00000e+02 2.01358e-01 -9.10270e+03
ERR DEF= 0.5
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-562.676 FROM MIGRAD STATUS=CONVERGED 97 CALLS 98 TOTAL
EDM=3.05398e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 N1 2.06784e-05 7.74025e-01 9.17634e-04** at limit **
2 N2 1.00766e+02 1.00765e+01 1.62161e-04 -1.92888e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 2 ERR DEF=0.5
6.404e-05 -6.052e-05
-6.052e-05 1.015e+02
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2
1 0.00075 1.000 -0.001
2 0.00075 -0.001 1.000

** 7 **SET ERR 0.5

** 8 **SET PRINT 1

** 9 **HESSE 1000

COVARIANCE MATRIX CALCULATED SUCCESSFULLY
FCN=-562.676 FROM HESSE STATUS=OK 10 CALLS 108 TOTAL
EDM=3.05312e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 N1 2.06784e-05 7.74030e-01 1.83527e-04 -1.57051e+00
WARNING - - ABOVE PARAMETER IS AT LIMIT.
2 N2 1.00766e+02 1.00765e+01 3.24322e-05 1.00938e-01
ERR DEF= 0.5
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 2 ERR DEF=0.5
6.404e-05 -3.080e-05
-3.080e-05 1.015e+02
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2
1 0.00038 1.000 -0.000
2 0.00038 -0.000 1.000

** 10 **MINOS 1000 1

THE NEGATIVE MINOS ERROR OF PARAMETER   1, N1 EXCEEDS ITS LIMIT.

MINUIT WARNING IN MIGRAD
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
FCN=-562.676 FROM MINOS STATUS=SUCCESSFUL 28 CALLS 136 TOTAL
EDM=3.05312e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER PARABOLIC MINOS ERRORS
NO. NAME VALUE ERROR NEGATIVE POSITIVE
1 N1 2.06784e-05 7.74030e-01 at limit 7.57280e-01
WARNING - - ABOVE PARAMETER IS AT LIMIT.
2 N2 1.00766e+02 1.00765e+01
ERR DEF= 0.5

** 11 **MINOS 1000 2

MINUIT WARNING IN MIGRAD
============== VARIABLE1 IS AT ITS LOWER ALLOWED LIMIT.
FCN=-562.676 FROM MINOS STATUS=SUCCESSFUL 23 CALLS 159 TOTAL
EDM=3.05312e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER PARABOLIC MINOS ERRORS
NO. NAME VALUE ERROR NEGATIVE POSITIVE
1 N1 2.06784e-05 7.74030e-01 at limit 7.57280e-01
WARNING - - ABOVE PARAMETER IS AT LIMIT.
2 N2 1.00766e+02 1.00765e+01 -9.72572e+00 1.04374e+01
ERR DEF= 0.5
[#1] INFO:Minization – RooMinimizer::optimizeConst: deactivating const optimization
[#1] INFO:Plotting – RooAbsPdf::plotOn(sumPdf) directly selected PDF components: (pdf_signal,pdf_bg)
[#1] INFO:Plotting – RooAbsPdf::plotOn(sumPdf) indirectly selected PDF components: ()
[#1] INFO:Plotting – RooAbsPdf::plotOn(sumPdf) directly selected PDF components: (pdf_bg,pdf_signal)
[#1] INFO:Plotting – RooAbsPdf::plotOn(sumPdf) indirectly selected PDF components: ()
[#1] INFO:Plotting – RooAbsPdf::plotOn(sumPdf) directly selected PDF components: (pdf_bg)
[#1] INFO:Plotting – RooAbsPdf::plotOn(sumPdf) indirectly selected PDF components: ()

6

Hi,
The advantage that the log is more readable in Minuit2 (at least for me) and please do not add as normal text , but either as an attached file or in a pre-formatted text field

Lorenzo

7

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