- 4pts Recall The Poisson Change Point Example On The Coal Mine Explosion Data See Week 12 Lectures Or Textbook 9 5 1 (97.45 KiB) Viewed 22 times
y=floor(coal[[1]])
y=tabulate(y)
y=y[1851:length(y)]
(4pts) Recall the Poisson change point example on the coal mine explosion data (see Week 12 lectures or textbook $9.5). The code below loads the data and tabulates the number of disasters (Y/) in each year (i) from 1851 to 1962, where 1851 is year i = 1. library(boot) y=floor(coal [[1]]) y=tabulate(y) y=y(1851: length(y)] Assume that the rates of disasters differ before and after the change point (k = {1, 2, ..., 112}), that is: ? • Y; ~ Poisson(x) for i = 1, 2, ...,k; • Y; ~ Poisson() for i =k+1,..., n. The likelihood of (u, 1,k) is n L(u, , k;y) = (ILS) () II П tuet yi! Yi! i=k+1 Compute the maximum likelihood estimate of the parameter vector (1, 1,k). (Note: k is discrete, so you'll need to use grid search (at least for k).)