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Mange takk til samtlige for stor innsats i forbindelse med prosjektrapportene! Jeg synes kvaliteten er gjennomg?ende meget tilfredsstillende. N? gjenst?r firetimers skriftlig eksamen, torsdag 16/xii 9:00-13:00 (Store fysiske lesesal, Fysikkbygningen). Som avtalt tidligere er dette en eksamen uten bok, men hver kandidat kan ta med seg (a) en alminnelig kalkulator og (b) n?yaktig en side med egne h?nd- eller maskinskrevne notater (alts? ikke to sider av ett ark, men en A4-side). Kandidatene kan endelig meget gjerne skrive sine besvarelser p? norsk (bokm?l, riksm?l eller nynorsk), selv om oppgavesettet kun vil forelegge p? engelsk. Lykke til -- eksaminator & sensor er spente.

Thanks to everyone for considerable efforts regarding the project reports, for which I find the quality generally to be quite good. Next up is the four-hour written examination, Thursday 16/xii 9-13. As agreed upon earlier, this is a no book exam, but each candidate can brin...

Note that I have also recently uploaded a couple of R scripts: com22b (mcmc for normal mixtures), com27a (re Exam 2004 #2, mixtures), com28a (re Exam 2004 #1, Poisson forest), com34a (re Exam 2008 #1, reading).

The Exam Project (three exercises, four pages) is now made available. It requires the data set "babies". Note as explained in the text that each student needs to include the special pages "Page A" and "Page B" with his or her project. Good luck!

Pensum (curriculum):

1. All material covered during the course from Nils Lid Hjort's Exercises & Lecture Notes (2008 edition as well as 2010 edition).

2. From the Gelman, Carlin, Stern, Rubin book: Ch 1, 2, 3, 4, 11 (Sections 1-5), 14 (Sections 1-4).

1. Note that I have now uploaded Version C (ten pages) of the Exercises & Lecture Notes, including methods for computing the marginal probability of f(y) of data sets, needed for model comparison. The importance sampling method was explained in the lecture. I have also uploaded com18b (corrected version of com18a, bioassay analysis), com21e (Weibull for Egypt), and com22b (mcmc for normal mixture).

2. Exercises for Wed Nov 17: Nils Exam stk 4020 2004 #1 and 2.

3. Exam project will be made available Wed Dec 1 (or a day or two earlier), with deadline for handing in your written report Mon Dec 13; details later. There's also the four hour written exam Thu Dec 16.

4. Next week I start Ch 14, the final chapter in the course.

1. Today I described and discussed the basic Metropolis MCMC scheme for drawing samples from a posterior distribution. I plan to round off Ch 11 next week, and also have a finalised pensumliste (curriculum description) ready by then. Next week we also finalise details pertaining to the exam processes.

I note that the basic methodology for MCMC simulation of relevance for this course is more or less contained in Nils Exercises 13-17 in the stk 4050 collection from 2007. Find these & print them out for your convenience.

2. Exercises for Wed Nov 10: The rest of Exam 2008 #3, including the MCMC scheme for drawing samples from p(a,b|data). Also, use MCMC with uniform proposals to draw samples from respectively (a) the N(0, 1), (b) the mixture 0.5 N(-2,1) + 0.5 N(2, 1).

1. Today I rounded of Ch 4 (including the Bernstein--von Mises theorems) and started Ch 11 (with the rejection-acceptance simulation strategy). I also went through the bioassay analysis (see com18a) and Exam 2004 #3 (sicut cervus desiderat ad fontes aquarum, see com20a).

2. Exercises for Wed Nov 3: Exam 2008 #3. Also, use the rejection-acceptance algorithm to simulate 10^4 points from the standard normal using the Cauchy as proposal distribution.

Next week I intend to round off Ch 4 and start Ch 11. Exercises for Wed Oct 27 are as follows.

First analyse the bioassay experiment data used in the book (see e.g. p. 88-89). Your task is to provide the posterior distribution of gamma = LD50 in the logistic regression model p(x) = H(a + bx), with H the logistic transform, in the following four fashions. Provide for each approach the posterior median and a 90 percent credibility interval.

(a) Use flat priors for (a, b) and the quadratic approximation to the loglikelihood. (This is the "lazy Bayesian" approach.)

(b) Use flat priors for (a, b), but now with b nonnegative, along with the quadratic approximation. (This is the "semi-lazy Bayesian".)

(c) Use flat priors with a nonnegative b, as above, but with the exact posterior, using a (a, b) grid along with "sample". (This would be the "serious Bayesian with a grid approximation" method.)

(d) Finally use again flat priors with a nonneg...

As previously mentioned my presence appears to be needed at the SFI^2 evaluation committee meeting for parts of Wed Oct 20 -- so there will be only a one hour lecture on that day, 9:15 to 10:00. I will go through the Exam 2008 #1 exercise plus more on the techniques of Ch 4.

There is of course a full three hours teaching session next week, Wed Oct 27.

1. We have started going through Ch 4, with applications, illustrations and a couple of tangents. We also examined techniques for demonstrating, in suitable cases, that the minimax solution is unique (and hence admissible). We shall later meet cases where the minimax solution is not unique.

2. Exercises for Oct 20: Exam Project 2008 #1. Also: Study the book's "running example" starting on p. 88, with the bioassay data. Provide Bayesian analysis of the LD50 parameter, (a) using the normal approximation, starting with a flat prior for (alpha, beta); (b) using the normal approximation, starting with a flat prior but with beta nonnegative; (c) using the exact posterior, with this flat prior with beta nonnegative. For point (c) you may choose a dense grid and apply the "sample" simulator.

3. I am needed for parts of Wed Oct 20 at another meeting, and will come back in a little while to the time implications for that day's lectures.

1. I discussed risk functions, minimum Bayes risk, least favourable priors, and minimaxity, applying the methods to exhibit minimax methods for the normal and binomial cases. We also touched various issues related to Ch 3, and did exercises Nils 2008 #8, 9, 10, plus the one with the streetcars of San Francisco.

2. Details for the exam process, including the necessary bureaucratics pertaining to the PhD candidates, are finalised next week.

3. Exercises for Oct 6: Exam Project 2008 #2 (the Dr. Phil. A.T. List problem); Nils 2008 #12; and finally Nils 2008 #14(h), where you are free to use all the algebra and results from points (a)-(g).

1. This week I tended to further general details pertaining to both Chs 2 and 3, including the Jeffreys prior, Bayes risk and minimum Bayes risk, minimax strategies, etc. We also did Exercises #1, 4, 9, 10 from Ch 2 and #3 plus half of 6 from Nils 2008.

2. Exercises for Sept 29: Do the streetcars of San Francisco with three data points, 203, 98, 259, and with your own (informative) prior. Find posterior mean, median, and a 95% credibility interval for the number of streetcars. Then do Nils 2008 Exercises #8, 9, 10. These are on the theoretical side of the spectrum, but we shall rather soon tend also to the more practical side, as soon as we're inside Ch 3.

3. Some R script codes and some further 2010 Exercises will sonn be finished and put up on the course website.

4. Matters pertaining to the exam process (ten-day home project plus written exam plus something extra for the PhD students, as per Faculty rules) will be discussed next week.

1. Today we more or less finished Ch 2; next week we start with Ch 3.

2. Exercises to prepare for Sept 22: Exercises #3, 6,7 from Nils collection 2008; then #1, 4, 9, 10 from Ch 2.

1. Today I formulated, discussed, proved & illustrated the Master Theorem about Bayes procedures, pertaining to their optimality property for given data, model, loss function. We also went through Exercises #1(a)-(d) (2010) and #1 (2008). I'll put up the R code I used for the Poisson data exercise rather soon.

2. Exercises for Sept 15: as far as we get on this list: #1(e) from 2010 (with numerical integration), then #2, 3, 4(e), 6 from the 2008 collection. You should go through also points (a)-(d) of Exercise 4, and make sure you understand the relevant details, but we shall only do point (e) in class.

3. Next week I'll proceed lecturing with material that is becoming increasingly though not fully correlated with the book's Ch 2.

1. Today I gave a broad introduction to the course & its contents & likely sequence of events.

2. If I manage to get a visum to India (an event with lower probability than 1, according to the Indian Embassy today) there is no stk 4020 teaching next week, i.e. Wed Sept 1.

3. Exercises to prepare for Wed Sept 8: First Exercise #1 from the 2010 collection of exercises and lecture notes; then Exercises #1 and 2 from the 2008 collection.

Welcome to the course! The course book is "Bayesian Data Analysis" (2nd Edition), by A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin (Chapman & Hall/CRC, 2003), available in the book store. To the first order of approximation I intend to have the same basis curriculum as for Autumn 2008: Chs 1, 2, 3, 4, 11, 14. I'll also provide special extra notes and exercises during the course, also to be considered part of the curriculum.

Please check out the Autumn 2008 page for this course, where you'll also find the 18 page pdf file "Course Notes and Exercises", dated 1 December 2008.