Add a time-heterogeneous SIR model

[fritzo]

Addresses #2426

This adds an SIR model with time-varying response rate rho and reproductive number Re. The response rate is assumed to be piecewise constant, say depending on known testing capacity. The reproductive number undergoes Brownian motion in log space. The motivation is to handle real-world datasets where policy changes can effect reproductive number over time. Existing homogeneous models are a very poor fit.

Mechanically this introduces a new autovectorization strategy, which we might eventually generalize into a strategy for poutine.markov contexts. The strategy is to sample a time-batch of curr values as an dist.IndependentUniform(...), then truncate and pad to get a time-batch of prev values, and finally replay the model with a time-batch of (prev,curr) pairs (this only works for Markov window of 1; longer windows would require more states). I.e. this implements the common inference motif of converting a sequential directed Markov chain model to a batched factor graph model.

The new strategy supports a wide range of time-varying variables, both time-independent and Markov with window size 1. I see this as the last major feature of contrib.epidemiology before release.

Tested

• smoke tests
• added to examples/.../sir.py

[martinjankowiak]

great that this works!

it really is getting quite complicated though so it's probably good that the current phase of feature addition is coming to an end.