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Let's see -- I've uploaded R scripts com86a and com87a, concerning cigarettes and lung cancer, Nils Exercises 22-23; com88b, sicut cervus desiderat ad fontes aqarum, deer in forest, exam stk 4020 2004 no. 3; and com 90b, empirical Bayes for binomials, exam stk 4020 2004 no. 4. Send me a mail if something here isn't properly uploaded.

We meet one more time before the exam period sets in. We do Execise 1 from exam stk 4020 2004, and otherwise use the time for "repetition & summary" work, with an opportunity for questions & answers. I will also place a few more R scripts on the website of relevance for solving some of the earlier exam questions. I shall also produce the promised precise curriculum list (containing zero surprises, but detailing which of the book's subsections are defined as merely "cursory curriculum").

One more piece of information: For the four-hour written examination Monday December 9, one may not bring the course book, but each student is allowed to bring one page of handwritten notes in addition to an ordinary calculator (intended for essentially simple calculations illustrating a formula or two).

For Thu Nov 21, work through Exam stk 2004 no. 1, and 2(f), where you are to put a prior on (theta1,theta2) uniform on the triangle where theta2 > theta1. Also work out methods and programmes for handling a binomial analysis where the prior is of type p0 pi0 + p1 pi1, a mixture of two Beta distributions. Finally give me your distribution for the number of children Odin had (as we know, he had six boys), (1) where you take the boy probability p known and equal to 0.514, (2) where you more passively argue that the ways of the Gods might differ from those of the humans, taking p a uniform.

Otherwise we use the time in "repetition modus", recalling and discussing material from the earlier chapters.

For Thu Nov 14, go through Exam stk 4020 2004, no. 4 with the variant that you do full hierarchical Bayesian analysis for estimating the ten probabilities, starting with a flat prior for (k,p0) at "basement level"; then no. 3; then no. 2. I shall place my R script "com85a" on the website, pertaining to the tasks listed in exercise 4.

Thu Oct 31 I discussed various aspects of empirical Bayes and the Stein paradox, including risk function analysis. I also went through Exam stk 4020 2012 Exercise 3, with the Belgian laboratories. I am also uploading "com83c" pertaining to this exercise.

For Thu Nov 7, go through Exam stk 4020 2004 Exercise 4 (I've uploaded this particular exam project too), and Nils Exercises 22(f)-(h) and 23(h). I shall also use a bit more time on Ch 5 material in general.

As agreed on, on Thu Oct 31 we do the "Belgian laboratories" exam stk 4020 2012 exercise #3. I will also go through empirical Bayesian matters related to the "estimating many normal means" situation, and the Stein effect, cf. Nils exercises #24 and #25.

I will teach for only two hours on Thu Oct 31, as I give a "popular science" type lecture in Auditorium 2 at 12:15-13:00: Hvem skal få lov til å gå titusenmeter?

http://www.uio.no/om/samarbeid/skole/fagped-dag/program/?fagkode=MAT

1. Today Thu Oct 17 I discussed details related to the Exam stk 4020 2008 set, including the Abel envelopes problem with two more data points and the Gamma-Normal class of priors for use with various normal models. I also went through *the basics of Bayesian image reconstruction*, entailing simple Markov type prior models for the image and then Metropolis methods for simulating from the posterior image distribution. This will also be carefully written out qua "Nils Exercises and Lecture Notes" in a collection of such to be uploaded to this course website reasonably soon.

2. I have uploaded various R scripts. Check in particular com77a and com77b (about simulating from the prior and posterior image model, dim = 1) and com78a and com78b (about simulating from the prior and posterior image model, dim = 2). Also, note com72b for the Abel envelopes and com73a, com73b, com73c for the Egyptian lifetimes.

3. For Thu Oct 24,...

1. We have started Ch 3, with simulation methods for sampling from the posterior distribution, involving acceptance-rejection methods and MCMC. The curriculum for Ch 3 includes Sections 1, 2. 3, but only 3.4.1 and 3.4.2 from Section 4. From Ch 4, only Section 4.1 is inside the curriculum, and from this terrain some of the main methodology is spelled out in the Nils Exercises & Lecture Notes #22, #23.

2. For Thu Oct 17, we work through the rest of Exam stk 4020 from 2008, exercises 2, 3, 1. For the Abel envelopes, provide and compare *two* analyses: (a) based on the data avaiable per 2008, with R envelopes 280, 304, 308, 310, 328; (b) based on two more numbers that came to light in 2012, namely 314, 336.

3. Over the course of the coming days I will be uploading a few R programmes on this website, pertaining to some of the exercises we're going through.

4. Free cake Tue Oct 15: The Sverdup Prize and distributions of confidence:
https://sites.google.c...

1. I'm in Oxford for the first week of October, so there is no teaching for stk 4021 Thu Oct 3:
http://www.stats.ox.ac.uk/Events/corcoran_memorial_lectures

2. For Thu Oct 10, work through as much of the Exam stk 4020 2008 set as you manage. We shall discuss these, first #2, then #3(a)-(e), then #1. Also read through Sections 3.3, 3.4, as these, with MCMC, will be worked with next.

3. Free pizza Tue Oct 8: Nate Silver's Bayesian methods for predicting election results:
http://www.uio.no/studier/emner/matnat/math/STK1110/h13/beskjeder/gaa-paa-populaervitenskapelig-statistikk.html

4. Free cake Tue Oct 15: The Sverdup Prize and distributions of confidence:
https://sites.google.com/site/nsfoslo/forside/diverse/sverdrupprisen-2013

5. Jeg vil sette pris på om den studenten som underveis i undervisningen torsdag 10/10 spurte meg om hierarkiske modeller kan sende meg en mail.

The exam will have two parts. Part I will be an "exam project", in the style of e.g. earlier Nils exam projects for stk4020 from 2012, 2010, 2008, which will be made open for downloading Fri Dec 6 and with deadline for handing in the reports Thu Dec 19. This part will in particular involve practical Bayesian analysis of real data. For those unable to deliver a hard-copy of the project in person it will be possible to send it electronically (ideally qua a pdf file attachment).

Part II is a four-hour written examination, taking place Mon Dec 9. Further practical details will be given later.

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. c...

Thu Sept 12 I went through Exercise 2.19 and Nils Exercise 12 (also with emphasis on mixture priors and their consequences), along with a bif of Nils Exercise 14 involving the Dirichlet distribution. I also discussed themes of Sections 2.2.

From Ch 2 the curriculum will be Sections 2.1, 2.2, 2.3, 2.4.1. For Thu Sept 19 I will round off this material, and perhaps have time to start Ch 3. Exercises to go through are as follows: Nils Exercise 14 (Gott würfelt nicht), Exam stk 4020 2010 #1.

Thu Sept 5 I went through various aspects of Section 2.1, including prior construction and prior elicitation, as well as general matters pertaining to Bayesian inference and the "Master Recipe" (cf. Nils Exercise #2).

For Thu Sept 12 I will go on to Sections 2.2 and 2.3, but the first of our three hours then will be devoted to discussion of exercises. First we (perhaps briefly) go through Exercises 1, 2, 3 from Ch 1. Then we do Nils Exercises 12 and 14(a), where you in the latter exercise ought to use results and the simulation recipe from Exercise 13. Finally, we do Exercise 19 from Ch 2.

Nils Lid Hjort

Nils Lid Hjort will step in and give the lectures on Thursday 5 september.

The course will start on Thursday 10.15 in room B71 (7th fllor, Niels Henrik Abels house)