Asymmetrical uncertainties for weighted histogram

[iaosiiuv]

Hello everyone. I had a small question about uncertainty representation for histograms.

When representing data, I saw that RooFit takes the frequentist approach to calculate uncertainties (with ROOT::Math::gamma_quantile), resulting in asymmetric uncertainties for each bin (as explained page 16 of this presentation).

I was wondering if we could do the same with MC. Usually MC distributions have weights for each events. Is this frequentist approach still valid? If no, what about if each event has the same constant weight?

More generally, can we estimate the new asymmetrical uncertainties of the weighted histogram by dividing the asymmetrical uncertainties of the unweighted histogram by the weights? This works with the sqrt(N) error, why not with the asymmetrical ones?

[moneta]

Hi,

RooFit (and ROOT optionally) uses classical Poisson confidence interval for binned data (see formula in PDG Statistics chapter, section 40.4.2.3 ), when the data are unweighted. In case of weights standard normal approximations are used and the errors are symmetric in this case. I would not use asymmetric errors for binned data. If the weights is probably just a scale factor, and constant, it is in this case correct to just rescale the obtained errors from the un-weighted case.

Lorenzo