Symmetrization of normalization uncertainty terms

TRExFitter Version and Commit Hash

current HEAD, TRExFitter version: v1.4.1-dev, Commit Hash: 700dada1

Description

Symmetrisation: ONESIDED currently symmetrizes normalization effects by varying nominal by the same relative amount in both the up and down direction. For a case of nominal = 1 and up = 1.05, it results in down = 0.95 (in practice: down = 2*nominal - up).

Another possible approach, which is more consistent with the effectively log-normal constraint term (Gaussian constraint + exponential extrapolation), would be to instead define the symmetrization differently. For \Delta = up - nominal, take the symmetrized version as 1 / (1 + \Delta). For the 5% variation example this comes out to a very similar number as in the current approach, but for larger variations the difference becomes more apparent. A 50% up variation symmetrizes to a 33% down variation. Another nice property of this approach is that it allows defining normalization uncertainties larger than 100% and then symmetrizing them and still ending up with positive templates.

I think this approach makes less sense for the symmetrization of shape variations, which we extrapolate linearly instead.

I have not fully thought through the potential interplay with AlternativeShapeHistFactory but I currently suspect nothing changes fundamentally with either of the two possible values of that option.

Reproducer Configuration

n/a

Ideas to Resolve

Implement a flag to switch the approach for symmetrization (per systematic or global?).