Hello Experts,
I have tried to work on the log-likelihood method. For that i tried the following example to do it using MINUIT.
https://root.cern.ch/doc/master/NumericalMinimization_8C.html
I did this with the simulation part.
I am not sure why my error bars are too large and PARAMETER CORRELATION COEFFICIENTS are close to 1.(this is not good)
I want to understand if this is a problem with how I work on the minimization (this is my first try of MINUIT) or something wrong with my function?
I would really appreciate it if you could help me.
some of the warnings also bother me.Please see part of my output.
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 alpha 9.62214e-01 2.32257e+00 -0.00000e+00 1.90820e+00
2 beta 1.18777e+00 1.67691e+00 0.00000e+00 2.28595e+00
3 gamma -1.57518e-01 1.55417e+00 -0.00000e+00 9.00438e-04
4 lambda 1.00000e+00 fixed
5 jQ2Bin 3.00000e+00 fixed
6 ixBin 1.00000e+00 fixed
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 3 ERR DEF=1
8.949e+00 -4.826e+00 3.385e-04
-4.826e+00 3.882e+00 -1.175e-03
3.385e-04 -1.175e-03 1.950e+00
ERR MATRIX APPROXIMATE
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3
1 0.81886 1.000 -0.819 0.000
2 0.81886 -0.819 1.000 -0.000
3 0.00063 0.000 -0.000 1.000
ERR MATRIX APPROXIMATE
Info in <TMinuitMinimizer::Minimize>: Finished to run MIGRAD - status 4
-LogLi[jQ2=03,ixB=01]= -13683.6712 from 25606 events
**********
** 100 **SET PRINT 2
**********
**********
** 101 **SET NOGRAD
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 alpha -5.00000e-01 2.00000e-01 no limits
2 beta 2.00000e+00 2.00000e-01 no limits
3 gamma 0.00000e+00 2.00000e-01 no limits
4 lambda 1.00000e+00 1.00000e-01 no limits
**********
** 102 **FIX 4
**********
FCN= unknown FROM FIX STATUS=RESET 0 CALLS 0 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS PHYSICAL LIMITS
NO. NAME VALUE ERROR NEGATIVE POSITIVE
1 alpha -5.00000e-01 2.00000e-01
2 beta 2.00000e+00 2.00000e-01
3 gamma 0.00000e+00 2.00000e-01
4 lambda 1.00000e+00 fixed
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
5 jQ2Bin 3.00000e+00 3.00000e-01 no limits
**********
** 103 **FIX 5
**********
FCN= unknown FROM FIX STATUS=RESET 0 CALLS 0 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS PHYSICAL LIMITS
NO. NAME VALUE ERROR NEGATIVE POSITIVE
1 alpha -5.00000e-01 2.00000e-01
2 beta 2.00000e+00 2.00000e-01
3 gamma 0.00000e+00 2.00000e-01
4 lambda 1.00000e+00 fixed
5 jQ2Bin 3.00000e+00 fixed
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
6 ixBin 2.00000e+00 2.00000e-01 no limits
**********
** 104 **FIX 6
**********
FCN= unknown FROM FIX STATUS=RESET 0 CALLS 0 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS PHYSICAL LIMITS
NO. NAME VALUE ERROR NEGATIVE POSITIVE
1 alpha -5.00000e-01 2.00000e-01
2 beta 2.00000e+00 2.00000e-01
3 gamma 0.00000e+00 2.00000e-01
4 lambda 1.00000e+00 fixed
5 jQ2Bin 3.00000e+00 fixed
6 ixBin 2.00000e+00 fixed
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 alpha -5.00000e-01 2.00000e-01 -2.00000e+00 2.00000e+00
2 beta 2.00000e+00 2.00000e-01 1.00000e-01 5.00000e+00
3 gamma 0.00000e+00 2.00000e-01 -1.00000e+00 1.00000e+00
**********
** 105 **SET ERR 1
**********
**********
** 106 **SET PRINT 2
**********
**********
** 107 **SET STR 1
**********
NOW USING STRATEGY 1: TRY TO BALANCE SPEED AGAINST RELIABILITY
**********
** 108 **MIGRAD 0 0.01
**********
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION. STRATEGY 1. CONVERGENCE WHEN EDM .LT. 1.00e-05
FCN=24.1591 FROM MIGRAD STATUS=INITIATE 43 CALLS 44 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 alpha -4.99992e-01 2.00000e-01 3.92610e-06 2.84471e+09
2 beta 2.00000e+00 2.00000e-01 0.00000e+00 3.51002e+09
3 gamma 0.00000e+00 2.00000e-01 0.00000e+00 1.46233e+10
4 lambda 1.00000e+00 fixed
5 jQ2Bin 3.00000e+00 fixed
6 ixBin 2.00000e+00 fixed
NO ERROR MATRIX
FCN=24.1351 FROM MIGRAD STATUS=PROGRESS 57 CALLS 58 TOTAL
EDM=4.36773e+08 STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 alpha -4.99992e-01 2.00000e-01 -1.23382e-08 3.62489e+09
2 beta 2.00000e+00 2.00000e-01 -9.99999e-09 4.04525e+09
3 gamma -2.40051e-09 2.00000e-01 -2.40051e-09 1.46233e+13
4 lambda 1.00000e+00 fixed
5 jQ2Bin 3.00000e+00 fixed
6 ixBin 2.00000e+00 fixed
MINUIT WARNING IN MIGRAD
============== Negative diagonal element 3 in Error Matrix
MINUIT WARNING IN MIGRAD
============== 1 added to diagonal of error matrix
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
1.0000e+00 1.0000e+00 1.0000e+00
MIGRAD FAILS TO FIND IMPROVEMENT
START COVARIANCE MATRIX CALCULATION.
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-1.6773e+00 1.9449e+00 2.7324e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 1.680006 TO DIAGONAL.
FCN=-20040.5 FROM HESSE STATUS=NOT POSDEF 22 CALLS 104 TOTAL
EDM=1.53846e+07 STRATEGY= 1 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 alpha -1.98192e+00 2.96355e+00 1.42060e+04 2.30764e+00
2 beta 8.58256e-01 4.46416e+00 1.58534e+04 2.61951e+00
3 gamma -9.48033e-01 1.96391e+00 5.73087e+07 4.86973e-04
4 lambda 1.00000e+00 fixed
5 jQ2Bin 3.00000e+00 fixed
6 ixBin 2.00000e+00 fixed
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3
1 0.99864 1.000 0.998 0.998
2 0.99805 0.998 1.000 0.998
3 0.99861 0.998 0.998 1.000
ERR MATRIX NOT POS-DEF
MIGRAD FAILS TO FIND IMPROVEMENT
MIGRAD TERMINATED WITHOUT CONVERGENCE.
FCN=-20040.5 FROM MIGRAD STATUS=FAILED 114 CALLS 115 TOTAL
EDM=1.53846e+07 STRATEGY= 1 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 alpha -1.98192e+00 2.96355e+00 -0.00000e+00 2.30764e+00
2 beta 8.58256e-01 4.46416e+00 -0.00000e+00 2.61951e+00
3 gamma -9.48033e-01 1.96391e+00 -0.00000e+00 4.86973e-04
4 lambda 1.00000e+00 fixed
5 jQ2Bin 3.00000e+00 fixed
6 ixBin 2.00000e+00 fixed
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 3 ERR DEF=1
1.018e+05 6.108e+05 4.724e+08
6.108e+05 3.682e+06 2.839e+09
4.724e+08 2.839e+09 2.199e+12
ERR MATRIX NOT POS-DEF
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3
1 0.99864 1.000 0.998 0.998
2 0.99805 0.998 1.000 0.998
3 0.99861 0.998 0.998 1.000
ERR MATRIX NOT POS-DEF
Info in <TMinuitMinimizer::Minimize>: Finished to run MIGRAD - status 4
-LogLi[jQ2=03,ixB=02]= -20040.4778 from 34978 events
Thank You
Testing_Minimization_1.cpp (7.5 KB)
xBQ2binning.root (1.9 MB)