Minuit Parabolic Errors Smaller than both Minos Errors?

Hi,

I was doing some tests to understand exactly how Minuit computes the parabolic errors vs the Minos errors and I observed a strange result. Using my test, Minuit finds parabolic errors that are smaller than both Minos errors for all the fit parameters:

FCN=1.10038e-14 FROM MINOS STATUS=SUCCESSFUL 275 CALLS 363 TOTAL

                     EDM=8.9213e-11    STRATEGY= 1      ERROR MATRIX 
ACCURATE
  EXT PARAMETER                  PARABOLIC         MINOS ERRORS       
  NO.   NAME      VALUE            ERROR      NEGATIVE      POSITIVE  
   1  x            1.23000e+02   7.26365e+00  -1.30000e+01   2.60000e+01
   2  y            5.73000e+02   4.78688e+01  -4.50000e+01   7.50000e+01
   3  z            2.50000e+01   1.53528e+00  -3.00000e+00   5.00000e+00
                               ERR DEF= 0.5

What I do for this test is to simply ask Minuit to find the maximum of a multivariate Gaussian function with correlated variables and asymmetrical widths (I simply use a different width depending if the variables are smaller or greater than their expected fit values). I would expect Minuit to find the following correlation matrix:

        1.000000000
        2.338779e-01    1.000000000
        8.988122e-01    4.169567e-01   1.000000000

but the covariance matrix it returns,
        5.276059e+01    -2.782138e+01   4.362987e+00


        -2.782138e+01   2.291426e+03    1.611347e+01

        4.362987e+00    1.611347e+01    2.357071e+00

,gives the following correlations:
        1.000000e+00    -8.000878e-02   3.911778e-01


        -8.000878e-02   1.000000e+00    2.194311e-01

        3.911778e-01    2.194311e-01    1.000000e+00

Could someone explain me how such results from Minuit are possible? Is it simply because the 2nd derivative of my function is not continuous at the maximum (note that the first derivative is)? Is there another way I can use Minuit to evaluate the covariance matrix properly?

Thanks! Received on Thu Dec 03 2009 - 23:57:42 CET