Forecast function for `EpiAware`

[SamuelBrand1]

Current state of code

As per #239 we have a neat forecast function for models which have had inference on some time span $(1, T)$. The posterior chain can be used to condition the sampling of the model extended to a longer time span $(1, T + n)$. This is used in the analysis pipeline.

Lack of generality

The problem here is that under the hood there are hard coded options, which reflect our analysis plan but are too specific to promote this function to EpiAware.

Pain points:

• define_epiprob: hard codes in discretised Gamma distributions.
• Lack of testing in a wider range of settings.

Proposal

If we can fix these pain points then we can add this nice functionality to EpiAware.

[SamuelBrand1]

Worth noting that this forecast approach works for our use case but is not general!

https://github.com/TuringLang/Turing.jl/issues/2239#issuecomment-2144614352

[SamuelBrand1]

Does this

Worth noting that this forecast approach works for our use case but is not general!

TuringLang/Turing.jl#2239 (comment)

suggest that we move towards not having vectorised calls? e.g. no MvNormal calls?

[seabbs]

Yes. Do you know what implications this has (performance / limiting flexibility etc?)

[SamuelBrand1]

The main argument against would be AD performance; because known vector-form functions might have adjoints which are accessed rather than calculated.

[SamuelBrand1]

Flexibility would only be improved.