Test using pigeons.jl inference methods with EpiAware models

[SamuelBrand1]

The Pigeons.jl package exposes parallel tempering for Turing models. PT is considered an effective inference methodology for posterior distributions with complicated geometries, and the Pigeons.jl package looks very interesting.

Identifiability/complex posterior geometry problems abound in stats epidemiology so it would be good to look at pigeons.

[SamuelBrand1]

I think a good test case would be: https://cdcgov.github.io/Rt-without-renewal/dev/showcase/replications/mishra-2020/

As mentioned in the vignette, there is non-identifiability between the neg bin observation dispersion and the noise of the AR(2) process for $\log R_t$. It would be interesting to see how Pigeons.jl deals with that.

[seabbs]

I thought the most/more interesting element was being able to run across many cores at once?

[SamuelBrand1]

I don't think that the multi-core aspect is as exciting per se, its more that by having a lot of cores you can create a "communication" bridge between an easy to sample distribution and a hard to sample distribution via a large number of intermediate distributions.

However, its still MH... just from theoretical considerations I expect it to be outperformed by NUTS on a few cores for not-so-hard distributions. Happy to see some counter evidence though.

[SamuelBrand1]

Full disclosure: I'm talking about parallel tempering as I learnt about it back in the day. Pigeons also has AutoMala https://proceedings.mlr.press/v238/biron-lattes24a.html I need to get to the bottom of whether that is an alternate sampler or blended into their meta-algo.