Understanding MINUIT results

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)

Hi,

@moneta could you please have a look? Thanks!

Hi,
Your minimisation fails. This could be to many reason, one could be that the parameters are too correlated. Another possibility is an error or a bad numerical implementation of the objective function. I would check first the function you are passing with Minuit that is implemented correctly and give results as expected.
To decrease the correlation, you can try to re-parametrize the problem with parameters that are less correlated, or fix some of the parameter which are 100% correlated

Best regards

Lorenzo

Thank You,@moneta.
I will try this.