[Fix] corrected expected_chisquare by adding the number of priors

[PiaLJP]

The number of priors needs to be included in the expected chisquare, see eq. (D.9) in section "D.2 Priors and the Bayesian approach" in arXiv:2209.14188v2 ("On fits to correlated and auto-correlated data").
Note that the expected chisquare is now correct in the case of priors that are not correlated with the data fitted.
For correlated priors further alterations would be needed. (The covariance (from eq. (D.9)) is no longer be diagonal w.r.t the priors so you cannot just add the number of priors.)

[s-kuberski]

Hi Pia,

thanks a lot for adding this, it has been on my list for quite some time now.

I agree that, the code will still not be correct in the case where the prior is correlated with the data. This should be addressed at some point. I had started to implement the proper solution, but then I was hesitant because, in principle, also the notion of a correlated fit would then have to be changed to a covariance matrix that also covers the contribution of the priors, so both cases should be handled together.

For now, it is good to fix the obvious bug for the standard case of an external prior.

[s-kuberski]

Sorry, I closed this by mistake. Before merging it, would it make sense to write a small test that ensures thatchisquare_by_dof for an uncorrelated fit to uncorrelated data, including priors, matches chisquare_by_expected_chisquare?

[PiaLJP]

Thanks :) , I just added such a test, also included a combined fit example where I also hand over a cov without correlations, maybe it's a little redundant and the first fit to a constant is sufficient and I should delete the rest?

[s-kuberski]

Thanks for the addition! I think there is no need to remove anything. I had briefly thought about also doing a fit with two parameters and two priors, but I think it is sufficient as it is right now.