Homework exercise on MCMC - due Wed. Oct. 24 The purpose of this homework is to make sure you can run MCMC (so more or less like writing ml code that we did in week 3 of ml) plus make sure you have some understanding of the ir"t" model Given that we (you) will be using Simon Jackman's Winbugs code, this may be easier for you to do in Winbugs directly (at the cost that you have to be more careful about picking up the output). You will need to change the updater method (don't worry!), taking the new updater from Week 5 (Neal's updater file). On my box it goes in C:\Program Files\WinBUGS14\Updater\Rsrc, on your boxes, either mutatis mutandis or ymmv depending on your generation. (Alex will make sure this works in the lab.) The exercise is first done with Jackman's legislative scaling, as per the APSR article (winbugs odc file, just open it in winbugs and click on some arrows to see stuff) and then similar data and methods for Supreme Court judges (as data for today's exercise). The second exercise is to allow you a bit more freedom. Working in groups is fine, but, like typing, winbugs is not a group skill. 1. Legislatures a. Run and replicate Jackman's results. Do with 10000 iterations plus 1000 iterations burn-in, thinning by saving every 25th obs, giving 400 samples. This should take something over an hour in the lab.) b. Monitor a few interesting nodes (that is, a few members of Congress). What is happening over time. 2. Judges. a. Run Jackman's model as a baseline. Do with 40,000 iterations plus 10,000 iterations burn-in. Thin the output such that only every 100th iteration is stored. b. Monitor a few interesting nodes. What is happening over time. c. Suppose you forget to drop the burn-in period. What happens when you take all obs. d. Run 4 chains instead of 1. Monitor convergence. Do the results differ? Remember you need 4 different starting values (look at examples in GH). e. Going back to a, run model with 1000 iterations plus 100 iterations burn-in and then with 10000 iterations plus 1000 iterations burn-in. Do the results differ? f. Going back to a, change the priors to be a lot less gentle. Do this by increasing precision by a factor of 100 and then perhaps even 10,000. What happens? What if you decrease prior precision by a factor of 100? g. Going back to a, change the two judges who are fixed. What happens? Interpret. h. Same question as g, but just flip Jackman's -1 and 1 assignment for the lefty and righty judges. i. Try running without assigning two judges to -1 and 1. What happens? j. Interpret the results from a and write a page or two (not a paragraph, not five pages) on what you learned about the Supreme Court, akin to the writeup by Jackman, et al in the APSR.