Exercises for Wed Oct 11

1. On Wed Oct 4 I spent some time discussing mixture priors and then the Bayesian take on the linear regression model, via the Gamma-Normal type priors, as used e.g. in Nils Exercise 23 with x = cigarette consumption and y = lung cancer death rates for n = 44 different US states. Note that I have placed the R script com25a on the site, with the basic computational details.

Then I started on Ch 4, and managed to convey 55% of the content of that chapter in one blackboard round. We'll use these results later on.

2. Note that we now have *two student representatives* and *a Facebook group* (see separate message).

3. I understand  that some students would appreciate *more details and more time* when I go through some of the exercises. I am contemplating giving those interested an opportunity to have *30 more minutes* for *a few* of the Wednesdays -- we take a break to 15:25 and start doing "more detail oriented going-throughs" for *a few* of the exercises (e.g. Exam Project exercises). The first time I try this (with any voluntary subset of the audience) will be in two weeks, Wed Oct 18.

4. Next week, Wed Oct 11, I'll be at the Odddays, the Odd Aalen symposium, and another of my PhD students, Sam-Erik Walker, will teach for me. He will focus on *going through exercises* (not on teaching more material).

5. Exercises:

(a) Consider again the (x,y) regression data for cigarette consumption and lung cancer death rates, from Nils Exercise 23. Plotting (x,y), it appears that Nebraska is somewhat different from the other states -- x = 42.40 is very high, but y = 23.03 is only moderate. Work out a cousin version of my com25a script which does the following. First, with the same prior as worked with there, carry out Gamma-Normal Bayesian analysis for the other n - 1 = 43 states (i.e. omitting Nebraska). Simulate 10^5 triples (alpha,beta,sigma) from that posterior distribution. Use this to assess the posterior distribution for delta = Pr(Y \le 23.03 | x = 42.40). Study the histogram of 10^5 values of delta, and determine whether Nebraska is a genuine outlier or not, regarding lung cancer and cigarette consumption.

(b) Do Exam stk 4020 from 2008, Exercise #1.

(c) Do Exam stk 4021 from 2015, Exercise #3.