Initialisation for epidemic inference

[SamuelBrand1]

This PR is for creating an appropriate initialisation for inference. In practice, this applies to the renewal model approach encapsulated by the Renewal model.

Major changes

• An new expectation is that any latent process model should pass an init kw value and this can have its own priors e.g. here:
  

  Rt-without-renewal/EpiAware/src/latent-processes.jl

  Lines 17 to 24 in dece834

  	init ~ latent_process_priors.init_rw_value_dist
  	σ_RW = sqrt(σ²_RW)
  	rw[1] = σ_RW * ϵ_t[1]
  	for t = 2:n
  	rw[t] = rw[t-1] + σ_RW * ϵ_t[t]
  	end
  	return rw, (; σ_RW, init)

• The callable function associated with an object which is a subtype of AbstractEpiModel is now fixed as defining the latent process -> infections transformation. Before it defined an updating function to be used by scan; however that was not the natural approach in (say) direct infection modelling. Instances of Renewal model now use scan under the hood. eg here:
  

  Rt-without-renewal/EpiAware/src/models.jl

  Lines 15 to 19 in dece834

  	@submodel latent_process, latent_process_aux =
  	latent_process(time_steps; latent_process_priors = latent_process_priors)
  	#Transform into infections
  	I_t = epimodel(latent_process, latent_process_aux)

• This change means that initialisation is also dealt with by the callable function. The only complex one is for Renewal here.
• For Renewal initialisation is done by treating init as defining a time zero incidence. The pre-time zero incidence is backwards exponential with the exponential growth rate implied by R_t[1] from the latent process and the GI. Note that this matches @dylanhmorris here. The difference is I use a quick Newton method with an informed guess to do the $\mathcal{R}_0$ to $r$ transformation; this is faster than using a generic root finder because you can solve the structure of the problem here and gets to high accuracy in a couple of steps: evidence here.

Minor change

• I've changed an Aqua kwarg to persistent_tasks = false because locally a Turing extension was precompiling out of sequence (TBD to burrow into that).

Closes #40

[seabbs]

This is really nice. I like the reorg. Some general comments about naming, docs etc which feel a little messy here.

I really like the use of $R_0$ here to define the initial growth rate and the approximation approach makes sense and seems correct. From a reviewer side though this really feels like another PR and would have been easier to review if that were the case. I can see why you included it here though.

In terms of the renaming etc I think I would again suggest we move many of these comments to issues so we can keep up the velocity. The only change I would really like to see here is an explicit test of the approximation approach.

[seabbs]

LGTM. Making an issue for internal functions now.