Extended simultaneous fit

Dear all,

I’m trying to perform an extended simultaneous fit of a pdf (gaussian signal + polynomial bkg) splitted in categories (using a RooSimultaneous).
According to the manual (v2.91, p17) I expect to obtain numbers of signal and bkg such that the sum, in each category, is equal to the number of generated events in each category.
This is exactly what I obtained if I fit the values of Nsig & Nbg (defined as RooRealVar) in each category.
Now, I would like to fit directly Nsig as a function of some parameters f interest. Nsig is now defined as a RooFormulaVar.

But when trying to perform such a fit, the result of the fit do not converge on values such that Nsig = Ngenerated - Nbg in any category. The difference is of the order of 2/1000.
Should I worry about it ? Is it an expected feature of the fit ? Why is the behaviour different between the two cases ?
Many thanks for the help.

Hi Aurelien,

If you make a non-trivial extended p.d.f, it is possible that there is some interaction between the extended term (which drives there normalization of Nexpected to Nobserved) and the normal likelihood (which drive the shape parameters) because the share e.g. parameters.

In your case, if Nsig is expressed in terms of parameters that also (indirectly) control one or more of the p.d.f. shapes, such correlations may cause that the minimum of the regular likelihood plus its extended term is in a place where Nobs!=Nexp.

If these deviations are small, and on average zero (check with a toy mc study), then there is no reason to worry.