Lecture & Exercises for Thu September 26

Thu Sept 19 I discussed Bernstein-von Mises theorems, concerning (a) the ML estimator thetahat being approximately N(theta0, Jhatinverse), with theta0 denoting the true parameter value, and (b) its Bayesian mirror statement, that theta given data is approximately N(thetahat, Jhatinverse). Here Jhat is the observed information matrix, minus the Hessian matrix of the log-likelihood function at the ML. I also went through Gott würfelt nicht, Nils Exercises 13, 14, and started discussing simulation strategies, at the start of Ch 3.

For Thu Sept 26 I shall go through Bayes Factors (from Ch 2) and proceed with more simulation techniques. Exercises to go through: Exam stk 4020 from 2012, #1, then #2 (a)-(b)-(c). This latter point involves programming the log-likelihood function, say logL(a,b,c), then using "nlm" of R to find its maximiser and the Hessian matrix. For comments & tricks pertaining to this task (a recurrent one, for the rest of our course), you may e.g. consult "Exercises and Lecture Notes" for the course STK 4160, 2011, specifically its Exercise 4. I also intend to write up a couple of more STK 4021 Exercises pertaining to these types of tasks.

Make sure you have printed out Exam project sets for STK 4020 for 2012, 2010, 2008.

Finally on the agenda for Thu 26/9 is to agree on exam dates, for the project part and for the four-hour written examination part.