Implement fit in Stan; fully Bayesian (including sigma); different smoothing. #34
Conversation
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Oh---one more difference (and this is probably the true source of the larger uncertainty and R_t values). I treat the time series of exponential growth as the mean of a Poisson distribution that describes each day's new cases (this is similar to Bettencourt & Ribeiro (2008), where Delta-T is a stochastic process and the observations are drawn from it, though there is no really good reason to assume that the draw is Poisson, I suppose); but your model uses the prior day's observed case number to predict the next, and only applies the stochastic process in the prior. I can imagine that my approach leads to a lot more uncertainty in the time-series R_t (since it is truly a stochastic process, observed only through the Poisson draws; while you assume that the prior day's observations---which are perfectly known---grow exponentially to produce R_{t+1}). |
1. Re-parameterized the model to efficiently fit states like NY where there is lots of data (i.e. the posterior is likelihood-dominated). It goes slower on the low-data states, but with fewer divergences / bad fits overall. 2. More discussion / description of the model *including differences to rt.live* in notebook, particularly the choice to have expected counts depend on yesterday's *expected* rather than *observed* counts. 3. Marginalize over the serial interval, based on work from https://epiforecasts.io/covid/
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See commit message for major update today; should still be merge-able automatically, but the model has gotten a bit more sophisticated, and there is a lot more explanatory text in the notebook about how it works. |
…t of days where the AR(1) prior dominates and days where the observational likelihood dominates.
Choose smoothing length scale to suppress power on scales of f > 1/(7 d) by an order of magnitude.
…ause most states total test data is crap.
…ed---most states above 1.
…ies and *then* add.
This may be a work in progress; I'm finding some differences in the analysis between my model and yours (in general, mine prefers larger values of R_t, particularly for the states with small values in your model). I think my model is also more conservative about the range of R_t, probably because I'm marginalizing over sigma, and sigma may not be particularly well determined (so sometimes the "smoothing" from small random increments in the prior for R_t is not as strong as yours).
Nevertheless, the should be safe to merge. Here is what I did:
I don't have the web skills to make the plots dynamical as your team does; but I did try to reproduce the "feel" of your plots for comparisons. Two key plots appear at the end of the notebook, and are reproduced here: