Tingene og verden

Wed 30 Jan we went through more basis materical of Ch 2 (ML analysis, delta method, stadard error estimation, confidence interval constructions, sandwich matrix) and also Nils Exercise #5. Note that I have uploaded com6a which deals with the details of that exercise.

For Wed 6 Feb, access the book webpage and get hold of the "birds on islands" dataset, and do the first parts of Nils Exercise #20, involving eight different Poisson regression models. Find the eight parameter estimates of mu(x0) = E(Y | x0), for the two values of x0 given there, also supplemented with standard errors and 90% confidence intervals for mu(x0). Use both "inverse information matrix" and "sandwich matrix" (cf. page 28).

Additional exercise: Invent and hold on to a certain density g(y) on (0,infty), e.g. of the type p1 dgamma(y,a1,b1) + p2 dgamma(y,a2,b2), to be considered the true density. Then for the five models of Nils Exercise #5, find the best parametric approximations and the associated minimum Kullback-Leibler distances d(g, model). Draw the five parametric approximations in a graph along with your g(y). -- For these calculations it is useful to use "integrate" in R, where integrate(something,a,b)$value provides the numerical value of the something function over the interval [a,b].