Next week I intend to ¡­

Next week I intend to round off Ch 4 and start Ch 11. Exercises for Wed Oct 27 are as follows.

First analyse the bioassay experiment data used in the book (see e.g. p. 88-89). Your task is to provide the posterior distribution of gamma = LD50 in the logistic regression model p(x) = H(a + bx), with H the logistic transform, in the following four fashions. Provide for each approach the posterior median and a 90 percent credibility interval.

(a) Use flat priors for (a, b) and the quadratic approximation to the loglikelihood. (This is the "lazy Bayesian" approach.)

(b) Use flat priors for (a, b), but now with b nonnegative, along with the quadratic approximation. (This is the "semi-lazy Bayesian".)

(c) Use flat priors with a nonnegative b, as above, but with the exact posterior, using a (a, b) grid along with "sample". (This would be the "serious Bayesian with a grid approximation" method.)

(d) Finally use again flat priors with a nonnegative b, but with the exact posterior, using the acceptance-rejection method given at the start of Ch 11. (This is the "serious and almost-exact Bayesian method".) One may alternatively use a MCMC simulation method, but the acceptance-rejection method is a bit easier here.

Then do Exam 2004 #3.