Thoughts for extending AutoGP/using AutoGP in larger model

[SamuelBrand1]

This is more a discussion point than an "issue".

Myself and @seabbs are really interested in using AutoGP inside of a larger project.

Rough concept

The rough concept would be to use AutoGP to power inference on the time-varying reproductive number of an infection process that we observe via eventual determined cases:

$$\begin{aligned} \log R_t &\sim GP_t \\\ I_t &= R_t (I \circ g)_t \\\ y_t &\sim \text{ObsKernel}(I_{t-1}, I_{t-2},...) \end{aligned}$$

where $R_t$ is the time-varying reproduction number, $I_t$ are the daily actual infections which depend on $R_t$ and the past infections smoothed by convolution with a vector g (aka the generation distribution), $y_t$ are the actual observations which depend on past infections via some observation kernel ObsKernel.

Feasibility of using AutoGP

The idea would be use AutoGP functionality, e.g. proposing/accepting-rejection of GP kernel compositions, inside a model structured as above.

Does anyone have a sense of how feasible that would be: my first past thought are not to fork AutoGP but rather to doing using and then pull out the bits of AutoGP under-the-hood code we'd want. We'd be declaring the probabilistic model described above in the Gen.jl PPL.