Asymmetric Parameter Constraints

[cverstege]

Question received via e-mail 📫:
Is it possible to add asymmetric parameter constraints in a fit? I can only find an option for symmetric parameter constraints in the documentation or the examples.

[cverstege]

It is possible, but as easy as you might think.

Short answer 💡:
If you can implement the fit resulting in those asymmetric uncertainties in kafe2, you can use the so called multifit. There is an example 📈 for this exact use case.
If the asymmetric uncertainty is provided externally, you either symmetrize it (of course by having a look at the likelihood and assess whether that's a reasonable approximation) or you have to perform the fit using your own likelihood.

Mathematical background 🎓:
In order to account for asymmetric parameter uncertainties, one needs to know the parametrization of the according likelihood resulting in the asymmetric parameter constraints.
Symmetric uncertainties always follow a Gaussian distribution, we can account for that easily in the final likelihood for the fit. This is not the case for asymmetric uncertainties any more. There are a lot of probability density functions (PDFs) having asymmetric shapes.
Since there's no easy way of providing the shape of the likelihood for asymmetric constraints, there is no implementation for that in kafe2 (yet).
Luckily, it is possible to account for the likelihood from other kafe2 fits. This can be done via the multifit functionality. By fitting the original fit which resulted in the parameter constraints together with the final fit for your parameters of interest (POIs), one can combine the Likelihoods for both fits and perform the fits simultaneously with shared parameters. This might even result in smaller uncertainties for the constrained parameter, as we have more data to use in the fit (in this case the second fit for the POIs) and better results overall.
There is an example 📈 doing exactly this and comparing the results of the multifit with the one using a regular parameter constraint.