not for merging: Explore divergent transitions

[sbfnk]

I've tried to explore the source of divergent transitions in the light of the discussion in #847
In order to do so I fixed parameters one-by-one to see the impact on divergent transition. This also gave an opportunity to experiment with modifying stan models from R.

A report is at
https://github.com/epiforecasts/EpiNow2/blob/explore-divergences/inst/dev/divergences.md

As found before, constraining the magnitude of the GP (alpha) seems to have the greatest impact on being able to fit the model. Even fixing the lengthscale the divergent transitions remain suggesting that alpha may be poorly identified in itself.

I don't think we need this to be added to the repo but if we think the general approach is of interest we could perhaps make it a blog post e.g. on the epiforecasts web site.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 6d69c39 is merged into main:

• ✔️default: 33s -> 29s [-24.8%, +0.4%]
• ✔️no_delays: 36.6s -> 42s [-2.92%, +32.54%]
• ✔️random_walk: 9.63s -> 10.4s [-3.29%, +20.03%]
• ✔️stationary: 18.7s -> 17.6s [-16.85%, +4.32%]
• ✔️uncertain: 53.2s -> 50.2s [-15.73%, +4.65%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[seabbs]

Really nice. The new stan from R tooling is looking great. I agree a blog post would be nice