Parameter error at the limit in Minuit

ROOT
1

Hello all

This question might not be proper for this forum.

After fitting(RooFit), I got this message from Minuit.

 FCN=4.25237 FROM MINOS     STATUS=SUCCESSFUL    857 CALLS        1068 TOTAL
                     EDM=9.16074e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                  PARABOLIC         MINOS ERRORS        
  NO.   NAME      VALUE            ERROR      NEGATIVE      POSITIVE   
   1  n_mc3        6.00455e+02   2.69257e+02  -2.72472e+02   2.69813e+02
   2  n_spin1      1.57043e+03   2.82148e+02  -4.88650e+02   2.80866e+02
   3  n_spin3      2.97256e-06   7.16673e+02   at limit      4.01967e+02
                                 WARNING -   - ABOVE PARAMETER IS AT LIMIT.
   4  n_spin5      2.15657e-02   6.16212e+03   at limit      4.74591e+02

I set the lower limit to 0 for n_spin3 and n_spin5 because they are the yields for some PDFs.
The values from the fit are at the limit of 0.
I think the parabolic errors for n_spin3 and n_spin5 are meaningless.
How can I get the right errors at the limit?

Thanks in advance.

2

I have mailed your problem to Wouter Verkerke. I hope that he will
give an answer soon.

Rene

3

Hi,

There is no trivial answer to this question as it more of a statistics issue than a software issue. General errors at boundaries are difficult to interpret.

In your case however I understand that your p.d.f is probably a sum of a number of shapes added with these coefficients that represent numbers of events. If so, you can consider the yields to go negative. Small negative values for coefficients in general do not lead to unphysical p.d.f.s as long as the sum of all p.d.fs times their coefficients is still larger than zero.
You can interpret a negative coefficient as a ‘depletion’ rather than an ‘excess’ (e.g. in a p.d.f like Nbkg*(flat-bkg)+ Nsig*Gaussian))
Once you do that the boundary is no longer there and both MINOS and HESSE should return a straightforward to interpret error.

Wouter