I have been trying to implement a pdf model that includes a binomial term to account for the unknown (but constrained) selection efficiency of an analysis that has been estimated with a finite size MC dataset…
Lets suppose I have an MC sample of 1million events, where my selection cuts give 900,000 events passing (90% efficiency). If this was part of a cross-section measurement, I might construct a likelihood as:
L = Pois(Nobs| Lsigmaeff)Gaus(eff|eff0,eff_err)
Where eff0 = 0.9, and eff_err could be my estimate for the uncertainty of the efficiency, which could just be the binomial error or something like that in this case. In this my “space point” is simply the number of observed events, Nobs.
So what I wanted to do was to do something more sophisticated: Make my “space point” Nobs and the number of selected events from the MC dataset (lets call it “n”). Then my likelihood would look like:
L = Pois(Nobs| Lsigmaeff)Binomial(n|N,eff)
Where N is a constant 1million (the number of trials) and n is 900,000 in my dataset.
So my problem is there doesn’t seem to be a way with the Roofit workspace factory to create this binomial term for my pdf. Technically I would also want the “n” variable to be a discrete, integer variable. But RooRealVar nor RooCategory seem appropriate for this sort of thing.
So is this at all possible with Roofit?