Beskjeder

The oral examinations of the candidates are taking place as follows. Please notify NLH immediately if you may have trouble with the assigned time point. (This particular message, with names of candidates etc., will be deleted some time after the exam.)

Thursday 18 December, in Room B 71:

1 09:30 -- 10:00 Rogelio Andrade Mancisidor

2 10:00 -- 10:30 Geir Gustavsen

3 10:30 -- 11:00 Qingsheng Dong

4 11:00 -- 11:30 J?rgen Hande

5 11:30 -- 12:00 Stian Solvang Johansen

6 12:00 -- 12:30 Ragnhild Bieltvedt Skeie

Friday 19 December, in Room B 91

7 09:30 -- 10:00 Sam-Erik Walker

8 10:00 -- 10:30 Hilde Galleberg Johnsen

9 10:30 -- 11:00 B?rd ?yvind Kvaal

10 11:00 -- 11:30 Mads Opstad Reistadbakk

11 11:30 -- 12:00 Hans Kristian Ruud

12 12:00 -- 12:30 Nathalie Charlotte St?er

13 13:30 -- 14:00 Dag Sverre Seljebotn

14 14:00 -- 14:30 Kjell Andreas Solberg

15 14:30 -- 15:00...

1. The Exam Project is now available; print out & start attacking it, good luck to all. Remember to deliver two copies of your report. Also make sure to include the two special pages with your reports (see page 1 of the Exam Project).

2. Send me a mail if anything might need a clarification. Also, in case I need to give any additional information at all, please check with this site's "beskjeder" once in a while during the project period.

3. If you have any time preference regarding the oral examination days December 18 and 19, please send me a mail, in order for this to be taken into account.

4. A list of students & timepoints for these oral examinations will be made available here by approximately Tue Dec 16 morning. (A week or so later that particular message will be removed from these public pages.)

Note: I have placed a further updated "Nils Exercises & Course Notes (Version C)" (dated 1 December 2008) on the site, with some further polishing of the previous version; this concerns some details of the Gamma-Normal machineries of Exercises 13 and 14, a "code" comment on the use of nlm for Exercises 18 and 19, and an extended version of Exercise 4. Again, please print out & keep among your notes (and this is the final version for Autumn 2008).

Also note: there was a small typo inside the "com58b" programme, which is now replaced by "com58d", which also utilises the "mvrnorm" method for simulating from a multinormal.

By Thu Dec 4 morning the Exam Set will be made available here, along with a certain "Self-declaration Page" that you need to print out and sign.

Note: I have placed an updated "Nils Exercises & Course Notes (Version B)" on the site; this 18-page version is then to replace the earlier 11-page Version A. Please print out & keep among your notes. Exercises 18 and 19 in particular go through the most useful approximation recipes associated with the large-sample theory of Chapter 4 (this chapter stops short of actually giving these recipes in a clear form).

Exam candidates are required to have learnt, or to learn, how these approximation recipes may be used, via programming of the log-likelihood function and consequent use of the nlm algorithm in R to find ML estimates etc.

Curriculum for this course:

* All of the "Nils Exercises and Course Notes" that we have been going through during the course. This also applies to the Exam set from 2004.

* From the Gelman, Carlin, Stern, Rubin book: Chs 1, 2, 3, 4 (minus section 4.3), 5 (sections 1-4), 11 (sections 1-5), 14 (sections 1.4).

* Geir Storvik's lecture of Mon 24 Nov, on "Bayesian objections to Bayesian statistics"; see the pdf file.

I have extended the "Nils Exercises and Course Notes" collection a bit and placed it on this website; please print out. A later version (to be completed within a week from now) will have a couple of more exercises.

Exercises for Mon Nov 24: Exercises 14 and 15 from the Nils collection (no. 14 is a more complete version of the extra exercise that appears on the message board from 18 Nov).

First exercise for Mon Nov 24 (more to be posted here within a day or two):

Go to http://lib.stat.cmu.edu/DASL/Stories/cigcancer.html, access the data set to create data vectors x = CIG (number of cigarettes sold per capita) and y = LUNG (death rate per 100,000) for 44 American states. Carry out a Bayesian linear-normal regression analysis for y on x. For sigma, let 1/sigma^2 have a Gamma prior such that sigma has 0.10 and 0.90 quantiles equal to 1.0 and 5.0. For alpha and beta, let these for given sigma be independent normals N(15, (2.0 sigma)^2) and N(0, (2.0 sigma)^2). Give 95% credibility intervals for the three parameters. Display the predictive distribution for ynew associated with a different state that has cigarette consumption xnew = 45.00.

Re-do the analysis with a noninformative prior.

Exercises for Mon Nov 17:

First: Use the Gibbs Sampler to draw 1000 samples (x,y,z) from the trivariate normal with means zero and covariance matrix Sigma, with rows (1,rho,rho^2), (rho,1,rho), (rho^2,rho,1), with rho = 0.777.

Then: Exam stk 4020 2004, no. 2, with this additional point: estimate theta with the loss function |thetahat - theta|^(3/2).

1. I have uploaded more R script files: com47b (Exam 2004, no. 3); com49a (binomial with a mixture prior for theta, and mcmc for simulations); and com50b (bioassay data analysis, with mcmc for posterior simulation of (alpha,beta)). Please try them out, and use local modifications to learn more.

2. There is an "invited lecture" for our course by Geir Storvik, to be given inside course hours Mon 24 Nov 10-11, on "Bayesian objections to Bayesian statistics" (!). His lecture is defined as part of the course curriculum.

Exercises for Mon Nov 10:

All of Exam stk 4020 from 2004, no. 3.

Let the prior for a binomial probability by 0.5 beta(2,8) + 0.5 beta(8,2), and assume n = 20 and y = 10 is observed. Generate samples from the exact posterior using (i) rejection sampling and (ii) a Metropolis mcmc algorithm.

Ch 11, no. 3.

Nils Lid Hjort gives an invited lecture at the SFI^2 Wed Oct 29 at 12:00 (see nr.no): "Feelings in Research: from Joy to Jealousy, from Anger to Depression (and More)".

Note that I have uploaded more R script files: com36c (exact vs. approximate posterior for Cauchy data), com40b (Poisson regression for airline accident data), com46a (Exam 2004, no. 4).

Exercises for Mon Nov 3:

Exam stk 4020 from 2004, no. 4: find ML estimates of (k, p0).

Use a modified version of com36c to assess exact and approximative posteriors for Cauchy data, with a couple of "strange" priors. How fast do data wash away the prior?

Finish 3.12, Poisson regression for airline data, with (a) normal prior-free approximation to posterior and (b) with the real prior that takes log(alpha) and beta to be independent normals N(log(20),sigma1^2) and N(0,sigma2^2), with values of sigma1 and sigma2 chosen by yourself.

Exam stk 4020 from 2004, no. 3.

Dates for the Exam Project: the exam set will be made available Thu Dec 4 in the morning, and the written reports need to be delivered (in duplicate) to the administration of the Mathematics Department by Mon Dec 15 (no later than 14:00).

Dates for the Oral Examination part: Thu Dec 18 and Fri Dec 19.

More practical details will be provided later.

Exercises for Mon Oct 27:

From Ch 4: 1, once more, with a general programme for n data points from a standard Cauchy; explore how quickly the normal approximation manages to work well, with the N(0.5, 2^2) prior.

From Ch 3: 12, continued.

Exam stk 4020 from 2004: we first round off No. 1 (check the R script file com45a), and then do No. 4.

Exercises for Mon Oct 20:

From Ch 4: 1, but now with a different prior for theta than the one given in the text, namely a N(0.5,2^2).

From Ch 3: 12, where you may use the R script file com43a as your point of departure for carrying out the required computations.

Exam stk 4020 2004 (check the course website for that year), No. 1.

I've now uploaded various "com" files with R scripts. Check them, try them out [using e.g. `source ("com43a")'], perhaps with some variations, to get acquainted with R scripts and their uses, including matters of plotting curves etc.

com files uploaded now include those used by Nils for numerical work associated with Exercises 2.8, 2.10, 2.11, 3.11, and the Nils extra one with Dirichlet analysis of multinomial data.

Exercises for Mon Oct 13:

From Ch 2: 17.

From Ch 3: 4, 11, 12.

From Ch 4: 1.

For the lecture part we continue with Ch 4.

Exercises for Mon Oct 6:

First: the rest of Exercise 2.13.

Then: go to http://lib.stat.cmu.edu/DASL/Stories/EstimatingtheSpeedofLight.html to find the 66 speed of light measurements from 1882, described in the book's Section 3.2. Assuming the normal (mu, sigma^2) model for these, apply the prior that takes sigma^2 an Inv-Gamma (1,10) and mu for given sigma a Normal (20, sigma^2/0.33^2). Simulate 10^5 realisations (mu, sigma) from the posterior. Give point estimates and 95% credibility intervals for mu, for sigma, and for the probability alpha that a new measurement will fall to the left of 12.5.

Then: redo the above with a more carefully constructed prior for sigma: let sigma^2 be Inv-Gamma (a,b), with parameters to reflect 0.10 prior quantile equal to 2.2 and 0.90 prior quantile equal to 18.8, for sigma.

Then: Exercises 17 and 22 from Ch 2, and 2 and 4 from Ch 3.

We have selected "tillitspersoner" for our course:

-- Ragnhild Bieltvedt Skeie, r.b.skeie@cicero.uio.no

-- Dag Sverre Seljebotn, dagss@student.matnat.uio.no

These can be contacted if there are special concerns pertaining to the course & its organisation, the teaching & lectures, etc. Of course such concerns may always be communicated directly to Nils -- but the "system" demands that we always have such tillitspersoner.

Mon Sept 29: we continue with Ch 3.

First: A die is thrown 100 times, resulting in respectively 15, 15, 17, 16, 13, 24 throws equal to 1, 2, 3, 4, 5, 6. Let the probability vector (theta1, ..., theta6) have a Dirichlet prior distribution with parameters (2,2,2,2,2,2). Carry out Bayesian inference for the parameters rho = theta6/theta1 and gamma = (theta2 theta3 theta4 theta5)^(1/4). Give in particular 95% credibility intervals for these two parameters and for their intercorrelation.

Exercises: From Ch 22, nos. 8, 12, 13, 22, 17.

To sample from a Dirichlet, use the fact that if G1, ... ,G6 are independent Gammas with parameters a1, ..., a6, then (G1/G, ..., G6/G) is a Dirichlet (a1, ..., a6), where G = G1 + ... + G6.

Mon Sept 22 we start on Ch 3.

Exercises: From Ch 2, nos. 8, 9, 10, 11, 12, 13, 22. For no. 10, you should do point (c), with a "serious" prior distribution, selected by yourself [sit still for five minutes and think about the cable cars of San Francisco, without consulting any further sources, and transform your thoughts into a well-defined prior for N]; and the extra point (d), which is to redo the calculations of (b) and (c) when I tell you that when I visited San Francisco in 2003, I actually saw three cable cars, not only one, and their numbers were 203, 77, 238. (Assume that these three sightings were independent of each other.)

Exercises for Mon Sept 15:

Nils Exercises: 7, 8.

Extra: (a) Generate ten data points from a Poisson with true mean 13.13. (b) Start with a Gamma prior (0.07, 0.07) for the mean parameter theta. Monitor how the posterior density is changing, from the 1st to the 2nd to the 3rd ... to the 10th data point, by doing the mathematics and writing a simple computer programme (e.g. in R).

From Ch 1, Exercise 9. From Ch 2, Exercises 1, 4, 10.

Exercises for Mon Sept 8: 2, 9 from Ch 1; Nils Exercises 6, 7, 8.

We will be spending some two weeks on Ch 2 and then some two weeks on Ch 3.

Exam form: The exam form for SKT4020 will be a project assignment and an oral exam. More information will follow.

For Mon Sept 1, we cross from "general introduction" to the book's Chapter 2.

Exercises for Mon Sept 1: Nils Exercise 3; from Chapter 1: 1, 2, 6, 9.