Add a factory for Poisson / NegativeBinomial / Binomial / BetaBinomial #2450
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fehiepsi
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Apr 28, 2020
| # pair of individuals results in an infection at this time step. | ||
| p = torch.as_tensor(R / N).clamp(max=1 - 1e-6) | ||
| # Combine infections from all individuals. | ||
| combined_p = p.neg().log1p().mul(I).expm1().neg() # = 1 - (1 - p)**I |
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I think this is not consistent w.r.t. before. Previously, combined_p is 1 - (e^-rate_s) ** I = 1 - (e^-p) ** I.
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That's right, I am changing the formula. This PR seems to make it more mathematically plausible.
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@fehiepsi I am not super confident in these formulas, but the plots do show they are at least in agreement. Let me know if you have any suggestions.
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This seems to be similar to Reed-Frost model. I agree that this formula seems to be more reasonable when N is small. Two formulas are similar when N is large (when p is small: e^-p ~ 1-p).
fehiepsi
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Apr 28, 2020
martinjankowiak
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Apr 28, 2020
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Addresses #2426
This creates a new helper
infection_dist()that creates one of a Poisson, NegativeBinomial, Binomial, or BetaBinomial depending on the quantitative values of its arguments. Of these four distributions, I intend only to use the Binomial and BetaBinomial; the others are present more as a bridge to limiting parameterizations that are more common in epidemiology.This PR also refactors the SIR and SEIR models to use the new helper. This refactoring prepares for overdispersed versions of these distributions in a follow-up PR #2451.
Tested
sir.py -p 10000 -d 60 -f 30 --plotas a sanity check