Allow to specify multiple convolution functions with CLI

[cschwan]

This will close #174.

TODO:

• migrate subcommand analyze; done in commit cfcf027
• migrate subcommand convolve; done in commit 1436618
• migrate subcommand plot; done in commit 1d4af96 and ddbf227
• migrate subcommand pull; done in commit a29639b
• migrate subcommand uncert; done in commit 5f8e576

[cschwan]

While converting some of the code to use the new ConvFun structs I stumbled upon a new question we need answer: how do we calculate PDF/FF uncertainties if two PDFs are given, for instance?

[cschwan]

While converting some of the code to use the new ConvFun structs I stumbled upon a new question we need answer: how do we calculate PDF/FF uncertainties if two PDFs are given, for instance?

To answer my question, it is instructive to think about the following situation: one PDF, one FF. In that case we now have two uncertainties: a PDF uncertainty and a FF uncertainty. In general we thus have an uncertainty associated to each one of the different convolution functions. We can calculate the uncertainty by varying the members of this set, while keeping the members of the other sets fixed (to the central member, for instance).

[felixhekhorn]

While converting some of the code to use the new ConvFun structs I stumbled upon a new question we need answer: how do we calculate PDF/FF uncertainties if two PDFs are given, for instance?

To answer my question, it is instructive to think about the following situation: one PDF, one FF. In that case we now have two uncertainties: a PDF uncertainty and a FF uncertainty. In general we thus have an uncertainty associated to each one of the different convolution functions. We can calculate the uncertainty by varying the members of this set, while keeping the members of the other sets fixed (to the central member, for instance).

I think for the moment this is what needs to be done - but I just wanted to point out that this might (or might not) be more complicated in principle: this assumes that the two ($N$) convolutions are uncorrelated (which for now they are). However, if one day we decide to fit PDF and FF simultaneously this assumption would fail and you would need to vary them consistently.

[cschwan]

[..] I just wanted to point out that this might (or might not) be more complicated in principle: this assumes that the two (N) convolutions are uncorrelated (which for now they are). However, if one day we decide to fit PDF and FF simultaneously this assumption would fail and you would need to vary them consistently.

Ah, that's a good point, thanks for pointing that out. In that case we will very likely need support from a convolution function library ('partons') that will tell us how exactly the uncertainty has to be calculated.