exercises for Wed Feb 17
1. On Wed Feb 10, Celine lectured on Ch 3, with the BIC and on hazard rate regression models. Nils went through some generalities and various details regarding Exam Project 2019, Exercise 1, the Swedish accidents dataset.
2. We've now placed on the course site (a) Celine's notes du jour, (b) Nils' "lecture 5" pdf, and (c) Nils' "com11a", the R script for the exam exercise. Run it, go through it, make sure you understand what goes on in its different parts, so that you may copy and modify for similar tasks later on.
3. Lars Henry Berge Olsen, mail address lholsen-at-math.uio.no, is our course's kurstillitsperson. We're a smallish group, so if you have concerns or comments (or advice!) to the course lecturers, you may by all means contact Celine or Nils directly -- but you may also go via Lars, so to speak.
4. We'll edit in here *exercises for Wed Feb 17*, pretty soon.
** (a) For Exam Project 2019, Exercise 1, the Swedish dataset, let x4 = 1 if year \ge 1967 and x4 = 0 if year \le 1966. Put this extra covariate into models M1 and M4, read off estimates and also 90 percent confidence intervals for the associated \beta_4 coefficient. Use both "under model" and "outside model" methods, and comment on your findings. Do this also for the model M1plus. -- For this work you may use bits & pieces of Nils' com11a, but propertly extended or modified.
** (b) Let p and q be the probabilities of Something Very Interesting, for two groups of people. The commonly accepted theory, which we all learn in school, is Model 0, that p = q, simply. Some controversialists claim however that Model 1 is better, that p \not= q. Suppose one observes x, binom(50, p), and y, binom(50, q), with x = 32 and y = 18. Take p = q a uniform, for Model 0, and take p and q independent and uniform, for Model 1, and set \pi_0 = 0.95, \pi_1 = 0.05, the prior probabilities for the two models. Do the Bayes calculations to determine the probabilities for the two models given the data. -- You may use this: \int_0^1 u^a (1-u)^b du = a! b! / (a+b+1)! .
Compute also the BIC scores and BIC approximations to the two posterior model probabilities.
Looping your programme suitably, let x run through all values from say 5 to 45, let y = 50 - x, and present Pr(Model 0 | x) and Pr(Model 1 | x) as curves. For which vaues of (x, y) = (x, 50 - x) will the skeptics need to accept the controversialists are right?