exercises for Wed Nov 17

1. We've been through most of 4-hour Exam stk 4021 from 2017, but I will do just a bit more on Wed Nov 17. 

2. Do Exercise 2, Exam project stk 4020 from 2012, about the gamma regression with (x_i, y_i). This may be seen as a prototype exercise for most of the themes of Ch 14. 

3. Then we do as much as we can with 4-hour Exam stk 4021 from 2013 (another Nils Exam set). 

4. Do a follow-up for the Exam stk 4021 blood group data, with counts 212, 103, 39, 148 for blood groups A, B, AB, O (for "ohne"). That exercise as about Theory Two Loci, with probabilities 

p(1-q), (1-p)q, pq, (1-p)(1-q) 

for the four groups -- and it is found to be wrong (!). Now do the similar thing for Theory One Locus (please do your Latin conjugations correctly), with probabilities 

p(2-p-2q), q(2-2p-q), 2pq, (1-p-q)^2, 

with (p,q) different from in Theory Two Loci, and with p + q < 1. 

Do maximum likelihood; compare maximised log-likelihood values; and throw it into a full Bayesian setup, with (i) prob(Theory One) = 0.50 and prob(Theory Two) = 0.50, and (ii) uniform priors for (p,q) in setup One and also for (p,q) in setup Two. Compute prob(Theory One | data) and prob(Theory Two | data).