Extended likelihood fitting with custom error level

Roofit and RooStats
1

Dear Root team,

Using RooFit in ROOT 5.22, I would like to do an extended likelihood fit with MINOS to a set of data at a certain error level (yielding e.g. a 5 sigma upper and lower limit, instead of the standard 1 sigma), and given a signal + background model. How do I set the error level AND make the fit extended? At the moment, the part of my code relevant to the question looks like this:

[code] RooAddPdf *spb = new RooAddPdf(“spb”,“spb”,RooArgList(*sig,*bkg),RooArgList(*fsig,*fbkg));

RooNLLVar spb_nll(“spb_nll”,“spb_nll”,*spb,*data,Extended(kTRUE));

RooMinuit m(spb_nll);
double errorLevel = 5.*5.*0.5;
m.setErrorLevel(errorLevel);
m.fit(“eh2”);[/code]

Is this the correct way to go? The result looks reasonable, but I can not judge whether the fit was actually extended or not, especially since I also tried a composite likelihood fit (i.e. excluding fbkg and Extended(kTRUE)) to the same data and got exactly the same result.

Many thanks in advance!

2

Hi,

(Sorry for the late reply - I just returned from vacation)

The code you show should work. The easiest way to see the effect of the
extended ML term is to compare numeric value of
the likelihood function constructed with and without extended option
e.g. ‘cout << spb_nll.getVal() << endl’

NB: Aside from RooFit technicalities there is a more fundamental statistics issue wether a delta-log-likelihood of 12.5 accurately represents a ‘5-sigma’ limit as this interpretation makes some assumptions on normal underlying distributions.

Wouter