Write and test a forecast function which projects inference forwards in time

[SamuelBrand1]

This PR implements a forecasting function for the pipeline. The idea behind this function is to use Turing.predict to sample from a model defined on a longer time interval conditional on an MCMCChains.Chain object that was generated by Bayesian inference.

There was a problem with this approach combined to vectorised random variables, but I've used "fix 1" from the issue I submitted to Turing TuringLang/Turing.jl#2239 .

NB: This PR should be strengthened with direct distribution tests on underlying forecast variables using HypothesisTests.jl. The reason this is not yet implemented is due to wanting to insert a test environment into the pipeline (this will be an issue).

Closes #231 .

[seabbs]

NB: This PR should be strengthened with direct distribution tests on underlying forecast variables using HypothesisTests.jl. The reason this is not yet implemented is due to wanting to insert a test environment into the pipeline (this will be an issue)

I suggest we make this a new issue/PR vs being blocked

[SamuelBrand1]

NB: This PR should be strengthened with direct distribution tests on underlying forecast variables using HypothesisTests.jl. The reason this is not yet implemented is due to wanting to insert a test environment into the pipeline (this will be an issue)

I suggest we make this a new issue/PR vs being blocked

Added an issue. Agree this is not a blocker.

[seabbs]

LGTM.

I think we should merge and open new issues to:

1. Add unit tests based on the new example/toy/test pipeline
2. Work to do to port core functionality into EpiAware (i.e. the method to extend epiproblems and a helper wrapper like generate_forecasts but with less dependence on configs).

I see some seemingly unrelated changes in define_epiprob. I don't love the hard coding of the generation time as Gamma but as this will shortly need a refactor when we merge in the changes to the infection module in EpiAware I think this approach is fine for now.

[seabbs]

I forgot to add but f2f @SamuelBrand1 and I have spoken about how great this functionality is in Turing - very exciting stuff.

[SamuelBrand1]

I forgot to add but f2f @SamuelBrand1 and I have spoken about how great this functionality is in Turing - very exciting stuff.

The Turing.predict functionality is really interesting.

[SamuelBrand1]

LGTM.

I think we should merge and open new issues to:

1. Add unit tests based on the new example/toy/test pipeline
2. Work to do to port core functionality into EpiAware (i.e. the method to extend epiproblems and a helper wrapper like generate_forecasts but with less dependence on configs).

I see some seemingly unrelated changes in define_epiprob. I don't love the hard coding of the generation time as Gamma but as this will shortly need a refactor when we merge in the changes to the infection module in EpiAware I think this approach is fine for now.

Agreed. The hard coded preference of the analysis we are doing is what is keeping this out of EpiAware atm.