Likelihood with weights for signal and NOT for background

Dear RooFit experts,

I’m carrying our an analysis in which I use a weighted unbinned extended maximum likelihood RooFit.
An objection to my analysis is that I’m applying the efficiency correction (deduced from the MC of my signal) to both signal and background.

Since the likelihood is generally a product of [signal pdf + background pdf] people asked me whether it’s possible to state in the likelihood to use the weights only for signal pdf and NOT for background pdf.

In other words they asked me whether it’s possible to build a likelihood that “chooses”, based on maximum probability, to use the weights only for the signal part and not for the background part.

To my knowledge this is not possible, or at least I wouldn’t how to do it.

Do you know whether this is possible ?
If yes, do you have an example from which I can learn ?


  • Mauro.

Hi Mauro,

I think this is mathematically not possible. The weight multiplies the log of the likelihood, e.g.

-logL = - sum(data) w_i log (S(x_i,p) + B(x_i,p))

for a pdf that consists of a sum of signal and background. The only way you can do this if you incorporate
the information that is contained in the event weights directly into your pdf of your signal and background,
but that’s non-trivial (and therefore people like to use weighted events)