Exploring SMC approaches to pyrenew

[SamuelBrand1]

Since I've stumbled onto https://pfjax.readthedocs.io/en/latest/notebooks/pfjax.html ...

I've got quite interested in whether a filtering approach to fitting and forecasting with pyrenew would be advantageous.

The basic idea would be that instead of sampling from MCMC, along with a long vector of innovation nuisance parameters, we hold/cache a particle filter of possible pyrenew states and hyperparameters (e.g. volatility of log Rt, feedback strength effect etc). Then as new data arrives we roll forward this particle filter using SMC^2 (i.e. particle filter and when particle diversity drops too low then refresh the hyperparams within the particles).

Advantages

• Set up would be expensive but then each new data arrival event would be fast
• Scales better with more time-varying latent processes

Disadvantages

• Less familiar approach; deviating from known community patterns e.g. EpiNow2
• Probable sensitive to how hyperparmeters "forget"/become less influenced by past data.