HGAM simulated data

[athowes]

The scope of this PR is to develop a notebook implementing simulated data which can be passed to a HGAM model. I'm making it in this repo, but mostly to use the review document capacity of GH. We could implement the results here too under this PR once we've agreed the data and fits look good.

I have written a plan for the work itself in the notebook.

My meta plan is:

1. Finish notebook (with review and agreement on results being nice)
2. Implement functions into RtGam
3. Implement tests into gamtools

Current rendered version: 2025-09-01_hgam.html.

Remaining

• The ST effects should be smooth over time and less spatially correlated
• The simulate_sir() function appears to be generating cases like 10^6. Must be a bug somewhere?
• When these are working, then need to get the forecast recovery to be good
• And the Rt recovery to be good

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[kgostic]

Left some high level comments! Would like ZS to look too before approving, and possibly BB!

[athowes]

Error in simulate_sir() where the value of S can be negative (allowing the value of I to be really high):