exercises for Tue Aug 27

1. Today, Tue Sep 20, we started the course!, and I gave a broad general introduction to the course & its themes. Again, the core currilcum will use (i) the Müller at al. book, Springer, 2005; (ii) the Nils intro chapter from "Bayesian Nonparametrics" (Hjort, Holmes, Müller, Walker, the 2010 Cambridge book); (iii) various things from the "Nils Collection" of Exercises and Lecture Notes.

2. Note that I've placed the Nils Collection and the Nils intro chapter at the course website, where there also will be other material in due course. In a week or two I plan also to go somewhat briefly through the BigInsight talk (2017) which is also placed there.

3. Exercises for Tue Sep 27 are as follows. First, as an extra exercise, assume y_0 is binomial (n_0, p_0) and y_1 is binomial (n_1, p_1), with y_0 = 33, y_1 = 44, from sample sizes n_0 = 100 and n_1 = 100. For priors, take p_0 and p_1 both uniform. (a) Give the Bayesian point estimate for \delta = p_1 - p_0, with loss function |\hat\delta - \delta|. (b) Then find the Bayes action, for the case where the action space is \{doingnothing, bigchange\}, and with loss function 

L( (p_0,p_1), doingnothing) = 1*(p_1 > p_0),

L( (p_0,p_1), bigchange) = k*(p_1 < p_0),

with k = 25.

Then do Nils Exercises 1, 39, 40. And have a look at the STK 9190 Exam Project Exercise 2, June 2018. -- It's useful here to know the basic formulae for conditional distributions for the multinormal. For the required details, consult Exercise 9 in the Nils Collection for STK 4021, 2018:
https://www.uio.no/studier/emner/matnat/math/STK4021/h18/exercises_stk4021_2017b.pdf