Exercises for Wed Oct 4

1. On 27th Nov I went through the rest of Ch 3, with various related details. I also did Exam stk 4020 2008 Exercise 2, the Abel Envelopes part, along with Nils Exercises 14a and 22.

2. Note the R scripts com20b, com22a, com23a. Go through them, run them, play with them by altering bits & pieces and see what happens with the results.

3. Next week I start Ch 4, about normal approximations, and links to maximum likelihood.

4. Exercises for next week:

** First: you throw your krone n = 25 times and observe y = 10 krone. Find the posterior density of theta = Pr(krone), along with "standard summary numbers", namely posterior mean, posterior standard deviation, 0.05, 0.50, 0.95 posterior quantiles, for each of the following priors:

(a) theta is uniform on (0,1) (which is where Thomas Bayes started, in 1763).

(b) theta is a Beta(c,c), with a high c, like c = 100.

(c) theta is a mixure 0.50 * uniform + 0.50 * Beta(c,c).

(d) theta is a mixture 0.50 * uniform + 0.50 * unit-point-mass-at-0.50.

** Then: Nils Exercise 23(h), with x = cigarette consumption and y = lung cancer death rates. Focus on "doing it" for these real data first; then go through points (a)-(g).

** If we find time: Exam stk 4020 2008, Exercise 1 (which is correlated with Nils Exercises 22 anad 23).