statisticalrethinkin..

294 11. COUNTING AND CLASSIFICATIONShould I include an explanation of why this is “natural”? Easiest derivation something like:Pr(y|λ) = λy exp(−λ).y!Take the logarithm of the density function, since any exponential family model can be pulledapart this way:log Pr(y|λ) = y log(λ) − λ − log(y!).To find the “natural” parameter of the distribution, find the coefficient that multiplies theoutcome, y. In this case, that is:log(λ).So the logarithm of the mean is the natural parameter of the Poisson. Could just put thisderivation in an endnote, instead.11.2.1. Example: Polynesian tool complexity. Data from Kline and Boyd 2010. 107 Hypotheses:(1) number of tools increases with population size, (2) number of tools increaseswith contact rate. Very small data set, so consider hazards of assuming posterior is normal.Will fit again later in book using MCMC and then compare. Also possibly a good RJMCMCexample, because will compute reasonably quickly (only 10 cases!).R code11.25library(rethinking)data(islands)d