# Some problem in minuit fitting, need your help!

Hi, Rooters:
I have met some problems in my fitting in which the Minuit is used. I really need you help!
my questions are:
1, the output information is copied below. Does my fitting work correctly judged by these output?
2，what is the meaning of “ERR MATRIX NOT POS-DEF” mentioned in the output information ?
3, what is the meaning of " PARAMETER CORRELATION COEFFICIENTS" matrix in the end of the utput?
The values of GLOBAL are very close to 1. what does this imply?

4, why “HESSE” appears in the output? In my code, I haven’t execute the HESSE command. Does it execute automatically after thee MIGRAD command?

5, the most important things: I am seriously interested the parameter errors.
For example， my fitting function is y = f(x,C0,C1…C6), where C0,C1…C6 is 7 parameters.
I want to calculated the error of y. My simple idea is using the errors of C0,C1…C6 given by HESSE to get the propagation error of y。That is: y_Error= sqrt[(dy/dC0)^2Err_C0^2+…(dy/dC6)^2Err_C6^2], in which dy/dCi(i=0,6) is the partial derivative of y respect to Ci.
Is it correct ? Do I need to consider the parameter correlation?

Thank you!!

Ps:The output information:

PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 C0 1.91712e+01 1.00000e-02 no limits
2 C1 -3.63544e-02 1.00000e-02 no limits
3 C2 -1.05223e+01 1.00000e-02 no limits
4 C3 -3.63538e-02 1.00000e-02 no limits
5 C4 9.66959e+02 1.00000e-02 no limits
6 C5 4.46961e-01 1.00000e-02 no limits
7 C6 1.03263e+01 1.00000e-02 no limits

** 1 **SET PRINT 2

** 2 **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.
START MIGRAD MINIMIZATION. STRATEGY 1. CONVERGENCE WHEN EDM .LT. 1.00e-04
FCN=4.1513 FROM MIGRAD STATUS=INITIATE 32 CALLS 33 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 C0 1.91712e+01 1.00000e-02 1.00000e-02 4.82435e-05
2 C1 -3.63544e-02 1.00000e-02 1.00000e-02 3.02295e-02
3 C2 -1.05223e+01 1.00000e-02 1.00000e-02 4.82445e-05
4 C3 -3.63538e-02 1.00000e-02 1.00000e-02 -1.60345e-02
5 C4 9.66959e+02 1.00000e-02 1.00000e-02 -3.48501e-07
6 C5 4.46961e-01 1.00000e-02 1.00000e-02 -2.02234e-04
7 C6 1.03263e+01 1.00000e-02 1.00000e-02 2.98532e-05
NO ERROR MATRIX
FCN=4.1513 FROM MIGRAD STATUS=PROGRESS 48 CALLS 49 TOTAL
EDM=1.94851e-08 STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 C0 1.91712e+01 1.00000e-02 -3.59611e-05 2.90554e-07
2 C1 -3.63545e-02 1.00000e-02 -5.60077e-08 -5.31095e-02
3 C2 -1.05223e+01 1.00000e-02 -3.59606e-05 2.88442e-07
4 C3 -3.63537e-02 1.00000e-02 9.82328e-08 2.98281e-02
5 C4 9.66961e+02 1.00000e-02 1.94464e-03 -8.18504e-07
6 C5 4.47015e-01 1.00000e-02 5.35534e-05 -5.22694e-05
7 C6 1.03263e+01 1.00000e-02 -1.90321e-05 7.40282e-05
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
START COVARIANCE MATRIX CALCULATION.
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-7.6801e-06 1.2667e-04 4.0675e-04 1.7475e-02 9.2812e-02 7.2952e-01 6.1597e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.006167 TO DIAGONAL.
FCN=4.1513 FROM MIGRAD STATUS=CONVERGED 98 CALLS 99 TOTAL
EDM=2.788e-08 STRATEGY= 1 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 C0 1.91712e+01 8.11910e+00 9.78461e-04 2.90549e-07
2 C1 -3.63545e-02 1.28110e-02 1.54261e-06 -5.31678e-02
3 C2 -1.05223e+01 8.11661e+00 9.78444e-04 2.88443e-07
4 C3 -3.63537e-02 2.24270e-02 2.80509e-06 2.97700e-02
5 C4 9.66961e+02 7.29320e+02 4.61082e-02 -8.18504e-07
6 C5 4.47015e-01 1.94744e+00 5.83193e-04 -5.25352e-05
7 C6 1.03263e+01 7.75123e+00 9.04888e-04 7.42565e-05
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 7 ERR DEF=1
6.592e+01 -3.229e-03 -6.050e+01 8.384e-04 -6.482e+01 -1.179e+00 7.227e-01
-3.229e-03 1.641e-04 -1.428e-03 2.480e-04 -9.375e-01 7.379e-03 9.580e-03
-6.050e+01 -1.428e-03 6.588e+01 3.689e-03 -7.289e+01 -1.115e+00 8.052e-01
8.384e-04 2.480e-04 3.689e-03 5.030e-04 9.470e-01 -7.405e-03 -9.679e-03
-6.482e+01 -9.375e-01 -7.289e+01 9.470e-01 5.319e+05 -4.179e+02 4.256e+03
-1.179e+00 7.379e-03 -1.115e+00 -7.405e-03 -4.179e+02 3.793e+00 4.158e+00
7.227e-01 9.580e-03 8.052e-01 -9.679e-03 4.256e+03 4.158e+00 6.008e+01
ERR MATRIX NOT POS-DEF
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3 4 5 6 7
1 0.99411 1.000 -0.031 -0.918 0.005 -0.011 -0.075 0.011
2 0.99412 -0.031 1.000 -0.014 0.863 -0.100 0.296 0.096
3 0.99410 -0.918 -0.014 1.000 0.020 -0.012 -0.071 0.013
4 0.99365 0.005 0.863 0.020 1.000 0.058 -0.170 -0.056
5 0.99453 -0.011 -0.100 -0.012 0.058 1.000 -0.294 0.753
6 0.96303 -0.075 0.296 -0.071 -0.170 -0.294 1.000 0.275
7 0.99447 0.011 0.096 0.013 -0.056 0.753 0.275 1.000
ERR MATRIX NOT POS-DEF

Hi,

2. Your fit converged, but your error matrix has problems because it was make positive defined. Now if the function is in aright minimum, the matrix must be positive defined by definition. So this is often indication of some problems

3. Here is the definition of correlation:

Here of the global correlation coefficient, which measure basically the correlation between variable i and all the others:

The fact that the values are close to 1 is not good. The parameters are too correlated, this also may cause the problem you have in (2)

1. Hesse is often run at the end of the minimisation to check the function minimum and compute correctly also the edm (expected distance from the minimum)

2. Yes, it is correct (in the limit of Gaussian errors), but you need to consider also the parameter correlations

Best Regards,

Lorenzo

Dear Lorenzo:
thank you!
as you mentioned, my fitting have some problems in not-positive-defined and correlations.
I am trying to find the reasons and solve them. I still have some difficulties.

1. In fact, the number of my 4 groups of data are: 116, 20, 20, 20. I get the same message "NOT POS-DEF " and similar correlation coefficients (close to 1) in these data fitting using the same 7-parameter formula. I can not understand why the parameters is so highly correlated since the number of my data points are more than that of parameters. How can I solved this problem?

2. Except the high correlations of parameters, Is there any other reason that causes the not positive defined? What can I do?

thank you once again!

Dear Lorenzo:
thank you!
as you mentioned, my fitting have some problems in not-positive-defined and correlations.
I am trying to find the reasons and solve them. I still have some difficulties.

1. In fact, the number of my 4 groups of data are: 116, 20, 20, 20. I get the same message "NOT POS-DEF " and similar correlation coefficients (close to 1) in these data fitting using the same 7-parameter formula. I can not understand why the parameters is so highly correlated since the number of my data points are more than that of parameters. How can I solved this problem?

2. Except the high correlations of parameters, Is there any other reason that causes the not positive defined? What can I do?

thank you once again!

Hi,

The parameter correlation is independent of the number of data points. It depends on how your fit function is defined. If the parameters are highly correlated the minimum is not anymore a point in the parameter space, but it becomes a line or an hyperplane, and therefore the minimization algorithm has problem to converge.
A re-parametrization of the parameters normally solves the problem.
An example is when using polynomial. If you are using standard polynomials, the parameters are strongly correlated, while if you use instead Chebyshev polynomials, they are orthogonals and their parameters will be much less correlated.
The first this for fixing your fit is therefore to make the parameter less correlated

Best Regards

Lorenzo

Hi

I cannot see the picture, could you re-sent it?

Best Regards!