Exercises for Wed Sep 20

1. On Wed Sep 13 we went through Exam stk 4021 2015 Exercise #1, and the extended streetcars in San Francisco exercise, with three datapoints y1 = 203, y2 = 157, y3 = 222, rather than only the first. I also pointed to various related issues. Then I rounded off Ch 2, with emphasis on the case of normal model + model prior giving normal posterior. See in this connection exercise (b) below, for next week.

2. I'm placing R scripts com18a (for Exam stk 4021 2015 Exercise #1) and com19b (for SFr streetcars) on the course website. Run them and make sure you understand what goes on.

3. Next week I focus on Ch 3, with multidimensional parameters. The basic concepts carry over from the one-dimensional case, but computational issues are going to be harder.

4. Exercises for Wed Sep 20:
(a) First, to the SFr streetcars one more time, now with *four* datapoints, 203, 157, 222, 314, using variations of my com19b programme, *and* where you construct your own prior.
(b) Then, do the following, with details. Suppose y | \theta is N(\theta,\sigma^2), with known \sigma, and with the prior N(\theta_0,\sigma_0^2) for \theta. Find the joint distribution of (\theta, y), as a binormal. Use Nils Exercise #9 to derive the posterior p(\theta | y). Then do this application: the IQ has a N(100, 15^2) distribution in the population. Albert checks his IQ using a simple test, with y | theta having a N(\theta,10^2) distribution. His IQ is measured to be 123 using this (not fully precise) test. Compute the posterior for Albert's IQ. Try other values and other variations.
(c) Finally, do Exam stk 4020 2008 Exercise #2, about the Abel envelopes of 1902. stk 4020 was a previous version of the present stk 4021 course, and you find the exam set on the appropriate course site, or here:
http://www.uio.no/studier/emner/matnat/math/STK4020/h08/exam_stk4020_2008.pdf

5. Very soon we're deciding on the time window [t_0, t_1] for the Exam Project, so check with the messages.