Tension between MINOS and MIGRAD fits

Roofit and RooStats
#1

Hello,

I am performing a fit with MINOS. The fitter first makes a call to MIGRAD in order to minimize the function. When this happens, MIGRAD returns a failed fit because the second derivative matrix is forced positive definite:

 MIGRAD FAILS TO FIND IMPROVEMENT
 MACHINE ACCURACY LIMITS FURTHER IMPROVEMENT.
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 MIGRAD TERMINATED WITHOUT CONVERGENCE.
 FCN=-212875 FROM MIGRAD     STATUS=FAILED        186         187 TOTAL

                     EDM=0.000123752    STRATEGY= 2      ERR MATRIX APPROXIMATE
maxNameSize = 22
  EXT PARAMETER                          APPROXIMATE        STEP         FIRST   
  NO.   NAME                  VALUE          ERROR          SIZE      DERIVATIVE 
    1 Pi0Pi0::amp1::f0_E1_re       -142.51        12.885        36.565    0.00015088
    2 Pi0Pi0::amp1::f0_E1_im       -356.26        24.627        7.9938    0.00049466
    3 Pi0Pi0::amp1::f2_E1_re        914.18        11.366        17.723    0.00022019

 EXTERNAL ERROR MATRIX.    NDIM= 100    NPAR=  3    ERR DEF=1
         166        189       92.9
         189        607        251
        92.9        251        129
ERR MATRIX APPROXIMATE
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3
      1:     0.637  1.000  0.594  0.634
      2:     0.898  0.594  1.000  0.898
      3:     0.906  0.634  0.898  1.000
 ERR MATRIX APPROXIMATE
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 MINUIT WARNING IN MIGRAD  
 ============== Negative diagonal element 1 in Error Matrix
 MINUIT WARNING IN MIGRAD  
 ============== Negative diagonal element 2 in Error Matrix
 MINUIT WARNING IN MIGRAD  
 ============== 1.41587 added to diagonal of error matrix
 MINUIT WARNING IN MIGRAD  
 ============== Negative diagonal element 1 in Error Matrix
 MINUIT WARNING IN MIGRAD  
 ============== 1.98679 added to diagonal of error matrix
 EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
       -0.4992892.49929 MINUIT WARNING IN MIGRAD  
 ============== MATRIX FORCED POS-DEF BY ADDING %f TO DIAGONAL. 0.501788
 MINUIT WARNING IN MIGRAD  
 ============== Negative diagonal element 2 in Error Matrix
 MINUIT WARNING IN MIGRAD  
 ============== 137.206 added to diagonal of error matrix

This then feeds into MINOS, which returns a successful fit:

FCN=-212875 FROM MINOS      STATUS=SUCCESSFUL    215         418 TOTAL

                     EDM=0.000211216    STRATEGY= 2      ERROR MATRIX ACCURATE 
maxNameSize = 22
  EXT PARAMETER                            PARABOLIC         MINOS ERRORS        
  NO.   NAME                  VALUE          ERROR      NEGATIVE      POSITIVE   
    1 Pi0Pi0::amp1::f0_E1_re       -142.51        14.608       -14.852        14.364
    2 Pi0Pi0::amp1::f0_E1_im       -356.26        29.163       -28.617        30.572
    3 Pi0Pi0::amp1::f2_E1_re        914.18        13.612       -14.014        13.566



Fit Status: 0
Error Matrix Status: 3

From several studies I have been doing, it appears as though MIGRAD does find the true minimum. Is it reasonable to trust the results of MINOS (a successful fit), if MIGRAD is having trouble?

I would greatly appreciate any suggestions as to how to better investigate this problem!