Time-varying parameters (i.e. conversion to latent variables)

[sbfnk]

Once #504 and #525 are done this opens the option of extending the distribution interface to allow any parameter to vary over time. An interface for Gaussian processes could e.g. look like

delay <- GP(mean = Normal(mean = 5, sd = 1))

for mean reverting GPs or

delay <- GP(init = Normal(mean = 5, sd = 1))

for GPs on first differences

A similar interface could be created for random walks (RW).

[sbfnk]

Would require quite a few changes to the underlying model(s) as PMFs would turn from vectors into matrices.

[seabbs]

We should have a chat at some point because this is feeling like interface -> internal vs epinowcast internals -> interface (i.e replicating the same functionality but in the other direction.

[seabbs]

I was thinking on read it that this was out of scope but now I look at it I don't agree with past Sam. This seems like a great feature to add. If we do want it then I think we should either choose to do #765 and then this issue or this issue and then that one. I think the ordering should be based on how much we want the features + effort to implement. My read is that this would be potentially easier than #765 and hence we should have a stab it it first. I think if we do want to tackle this then I think the first step is to make some subissues to break this down into easier chunks as its quite a big/hard feature to add with a lot of dangerous edge cases IMO.

[sbfnk]

In terms of design, I'm thinking it would require making the params vectors arrays/matrices and then use these (with repeated elements if static and otherwise time-varying). Main steps I think would need doing are, I think.

1. make GP/RW code more general
2. make param vectors matrices
3. integrate the two