Pure Poisson model versus gamma-Poisson model #21
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IIRC there is a bug in the stan implementation of dgampois (you can find its definition here https://rdrr.io/github/rmcelreath/rethinking/src/R/distributions.r . Probably rmcelreath/rethinking#53 is related. |
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I added a comment to the code in #31 mentioning about the bug. Thanks for raising this! |
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According to Chapter 12.1.2, a gamma-Poisson model should reduce the impact of high pareto-k points by accounting the difference in rates as gamma-distributed. Hence, highly influential points like Hawaii in the Oceanic tools dataset should not pull the low-contact trend down as much.
I have attempted to replicate Figure 12.2 that accompanies this statement, but I did not get the same result from the models built in numpyro, that the original book author presented. Between Pure Poisson model and gamma-Poisson model, the only observed difference I had was the larger dispersion that is accompanied with using a gamma distribution to estimate the Poisson rate. However, the mean prediction line is similar across both models.