statisticalrethinkin..

332 12. MONSTERS AND MIXTURESthe gamma-Poisson process. e numbers of accidents across days are highly variable, muchmore variable than a Poisson process can suggest. In particular, on days without the speedlimit (righthand plot), there is a very long tail of high accident numbers. On days with thespeed limit, this tail is greatly reduced, although there are still some days with more than40 accidents, even then. e gamma-Poisson distributions can cover this heterogeneity innumber of accidents, while the Poisson curves in both cases are far too narrow are symmetrical.You can simulate counts and directly estimate the probability of, say, 30 or more accidentsper day with and without the speed limit. is will help me show you how to workwith the posterior some more, as well as demonstrate that the speed limit has a more appreciableeffect on the variation than it does on the mean. Remember, the average number ofaccidents reduced by the speed limit is only 4. But let’s ask how much the upper tail gets reduced.Here is how we might compute the predicted proportions of days, with and withoutthe limit, with 30 or more accidents.R code12.41post