Covariance matrix from Minuit - all diagnol elements are = 1

Roofit and RooStats
1

Dear Experts,

I am trying to fit a histogram using Fit() method of TH1F. The fit result says
that it is converged.
To understand about the errors, I tried printing the covariance matrix using:
GetCorrelationMatrix() method and this is the output of 11x11 matrix:

     |       0    |       1    |       2    |       3    |       4    |
----------------------------------------------------------------------
   0 |          1     -0.5179  -8.214e-07      0.2176     -0.1181 
   1 |    -0.5179           1   4.893e-06     -0.3732      0.4191 
   2 | -8.214e-07   4.893e-06           1  -2.274e-06   5.223e-06 
   3 |     0.2176     -0.3732  -2.274e-06           1     -0.3278 
   4 |    -0.1181      0.4191   5.223e-06     -0.3278           1 
   5 |   -0.02698     -0.2906  -3.012e-06    -0.02109     -0.2678 
   6 |   -0.02138      0.3649   3.957e-06    -0.02319      0.2458 
   7 | -9.795e-05   0.0003813   5.308e-06  -0.0001973   6.453e-05 
   8 |     0.6152     -0.4815   1.111e-06   -0.001847      0.4564 
   9 |    -0.3408      0.6619   2.933e-06      0.1035       0.131 
  10 |    -0.4931       0.141  -3.338e-06    -0.05188     -0.6634 


     |       5    |       6    |       7    |       8    |       9    |
----------------------------------------------------------------------
   0 |   -0.02698    -0.02138  -9.795e-05      0.6152     -0.3408 
   1 |    -0.2906      0.3649   0.0003813     -0.4815      0.6619 
   2 | -3.012e-06   3.957e-06   5.308e-06   1.111e-06   2.933e-06 
   3 |   -0.02109    -0.02319  -0.0001973   -0.001847      0.1035 
   4 |    -0.2678      0.2458   6.453e-05      0.4564       0.131 
   5 |          1     -0.9733   -0.007536     -0.1272     -0.5273 
   6 |    -0.9733           1     0.01916     0.05245      0.5137 
   7 |  -0.007536     0.01916           1  -0.0001026  -9.541e-05 
   8 |    -0.1272     0.05245  -0.0001026           1     -0.4656 
   9 |    -0.5273      0.5137  -9.541e-05     -0.4656           1 
  10 |     0.2628      -0.194  -1.691e-05     -0.8442     0.04228 


     |      10    |
----------------------------------------------------------------------
   0 |    -0.4931 
   1 |      0.141 
   2 | -3.338e-06 
   3 |   -0.05188 
   4 |    -0.6634 
   5 |     0.2628 
   6 |     -0.194 
   7 | -1.691e-05 
   8 |    -0.8442 
   9 |    0.04228 
  10 |          1

[quote]In the root manual, it is mentioned that:
If no mitigating adjective is given, then at least Minuit believes the errors are accurate, although there is always a small chance that Minuit has been fooled. Some visible signs that Minuit may have been fooled:

Correlation coefficients very close to one (greater than 0.99). This indicates both an exceptionally difficult problem, and one which has been badly parameterized so that individual errors are not very meaningful because they are so highly correlated
[/quote]

Now I have two questions:
(1) As we can see that all the diagnol elements are = 1
Does it mean that its not a good fit?
If that is so how do I take care of this?

(2) This is what I understand: the Correlation coefficients can be negative bu the eigenvalues should be positive for minimisation. How can I retrieve the eigenvalues for this fit?

Thanks in advance,
Best Regards,
Shilpi

2

Hi,

What you have printed is the correlation matrix not the covariance matrix. The correlation matrix is defined from the covariance matrix:

corr(i,j) = cov(i,j)/ sqrt( cov(i,i) * cov(j,j) )

so the diagonal elements are 1 by definition.
Your correlation matrix looks then fine to me, there no correlation coefficients (i.e. off-diagonal elements) very close to 1.

Best Regards

Lorenzo

3

Hi Lorenzo,

Thanks a lot for making it clear.

Best Regards,
Shilpi