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1. I've uploaded com33b (for Exam 2012, Belgian laboratories), com34a (for Exam 2012, sure menn og blide koner), com35a (for old Egypt lifelengths, Nils Exercise 8, MCMC).

I'll also upload R scripts from Ida Scheel, for her exam project questions 2016.

2. Importantly, I've also uploaded the Four-Hour Exam set from December 2015. Work them through!

3. For Wed Nov 29 I'll first round off the Belgian laboratories, then go in "let's repeat what we've learned" modus, looking through the curriculum. I'll also answer queries and respond to comments etc. We may use part of the time to discuss points from the Four-Hour Exam set from 2015.

As usual (!), I'll also another half hour, 15:20 to 15:50, for those interested. You may send me questions in advance.

4. There's a Time Window modification for the Exam Project. It's being made available on *Thu Nov 30 before 12:00*, as agreed, but you're generously being another day before the deadline for handin...

1. On Wed Nov 15, Nils was busy with the FocuStat Research Kitchen ("From Processes to Models"), but Ida Scheel went through the main aspects of the Exam problems 1 and 2 from 2016.

2. For Wed Nov 22, go through as much as you can from the following. (a) Exam stk 4020 2012 Exercise #3, #1; (b) Nils Exercise 8. For the latter, carry out the analysis using (i) the normal approximation and (ii) MCMC.

3. I'm again offering an extra half hour, from 15:20 to 15:50, for extra questions, queries, details, etc. You may send a mail if there's anything in particular you might wish to have discussed or clarified.

http://www.uio.no/studier/emner/matnat/math/STK4020/h12/exam_stk4020_2012final.pdf

1. On Wed Nov 8 I discussed more MCMC, with emphasis on the Metropolis algorithm and its uses, and also the Gibbs sampler. I also went through various details related to Exam 2015, #2, the ensemble of geometric probabilities. Furthermore I touched general regression models, outside the classical linear regression framework.

2. On Wed Nov 15 I'm busy with the FocuStat Research Kitchen ("From Processes to Models). Ida Scheel will teach then, and use perhaps most of the time for going through the two Exam Project problems for 2016 (when Ida had this course).

3. On Wed Nov 22 there's another opportunity to take up details and queries, in an extra half hour 15:20 to 15:50.

4. A clear curriculum list will be uploaded shortly. About the only part still remaining for us is the first half of the regression chapter 14.

5. Earlier I've uploaded a file from Sam-Erik Walker, with details for Exam 2008 #1. I've now upl...

1. I've uploaded com29a, for a clear illustration of MCMC, for sampling from a given p(theta), here in dimension 1. Play with the a and b parameters to gain insight. Do the rest of Exam stk 4021 2015 #2, with your own MCMC for p(a,b|data).

2. I've also uploaded com30a, for Exam 2015, #2, an ensemble of geometric probabilities, where I also compute and compare *risk functions*. There'll be a follow-up com30b too, with MCMC.

3. On Wed 1, I went through basic MCMC theory, concentrating on the simple but general Metropolis algorith, I also did most of Exam 2015 #2, but not all.

4. For Wed 8, finish the remaining points of Exam 2015, #2, which involves setting up an MCMC for p(a,b | data) in that context.

5. On Wed 8 I'll do some more from Ch 5, along with some more MCMC. 

6. Also on Wed 8 Nils offers his time, from 15:20 to 15:50, for going through more details at a lower pace, answering questions, etc.

1. On Wed Oct 25, I went through two previous Nils Exam Project exercises -- 2004, #4, hierarchical Bayes for an ensemble of probabilities, and 2008, #3, lifetimes from Roman era Egypt, with Weibull. I also discussed general aspects of Ch 5, and spent a few minutes on the basic MCMC ideas.

Note that I've placed R scripts com27a and com28a on the website, for these two exam project exercises.

2. For Wed Nov 1, do Exam 2015 #2, another hierarchical model exercise. Also, attempt to set up an MCMC to simulate from the target density of type

p(theta) = 0.25*exp(-abs(theta-a0)) + 0.25*exp(-abs(theta+a0))

with a0 = 2.00. Do this by proposals theta[i+1] being a uniform on [theta[i] - b0, theta[i] + b0], where you try out a decent b0.

3. On Wed Nov 1, I will spend *some* time to round off the essence of Ch 5, and then talk on MCMC (the last Big Thing in the course).

4. On Wed Nov 1, we have an extra ha...

1. I've rounded off Ch 4 and started Ch 5, with an emphasis on hierarchical modelling for analysing an ensemble of parameters.
 I also went through Exam stk 4021 2015 #3, with change point analysis.

2. I've uploaded com26a and com26b, related to such Bayesian change point analyses.

3. For an interesting change-point analysis, where such Bayesian methods also could have been used, check Celine Cunen and Nils Lid Hjort's blog post, on the World's First Ever Novel (from the 1460ies, 150 years before Don Quijote):

www.mn.uio.no/math/english/research/projects/focustat/the-focustat-blog!/tirant.html

4. For next week, do the Egyptian lifetimes, from Exam 2008 #3, and the ensemble of probabilities, from Exam 2004 #4; this latter exam project has been uploaded to this site. Since my coauthor Gerda Claeskens have moved from A to B in Belgium, so has her website, with datasets from Claeskens and Hjort's Model Selection Book, where you may now find the...

1. I've attended the Odddagene, the syposium for Odd Aalen, Wed 11-12, and in loco Hjorti Sam-Erik Walker, one of my PhD students, went through a few exercises, including Exam stk 4020 2008 Exercise #1.

2. Next week, Oct 18, I'll round off Ch 4 and start Ch 5, on basic hierarchical modelling.

3. Exercises for Oct 18: First, Exam 2015, #3, about Bayes for change-points (and British mining disasters). Then, Exam 2008, #3, (a), (b), (c), (d), (g).

1. On Wed Oct 4 I spent some time discussing mixture priors and then the Bayesian take on the linear regression model, via the Gamma-Normal type priors, as used e.g. in Nils Exercise 23 with x = cigarette consumption and y = lung cancer death rates for n = 44 different US states. Note that I have placed the R script com25a on the site, with the basic computational details.

Then I started on Ch 4, and managed to convey 55% of the content of that chapter in one blackboard round. We'll use these results later on.

2. Note that we now have *two student representatives* and *a Facebook group* (see separate message).

3. I understand  that some students would appreciate *more details and more time* when I go through some of the exercises. I am contemplating giving those interested an opportunity to have *30 more minutes* for *a few* of the Wednesdays -- we take a break to 15:25 and start doing "more detail oriented going-throughs" for *a few* of...

1. We have two "student representatives":

Madeleine Innholt Halle - madeleine.innholt@gmail.com

P?l Sandnes - palgroth@gmail.com

If you wish to convey some views regarding the teaching or the course generally, you can of course contact me, Nils, directly -- but you may also approach the student representatives.

2. We have a Facebook group!, initiated by Madeleine, "STK4021 study group fall 2017". Join, read, contribute, use it.

https://www.facebook.com/groups/1469612959784992/

1. On 27th Nov I went through the rest of Ch 3, with various related details. I also did Exam stk 4020 2008 Exercise 2, the Abel Envelopes part, along with Nils Exercises 14a and 22.

2. Note the R scripts com20b, com22a, com23a. Go through them, run them, play with them by altering bits & pieces and see what happens with the results.

3. Next week I start Ch 4, about normal approximations, and links to maximum likelihood.

4. Exercises for next week:

** First: you throw your krone n = 25 times and observe y = 10 krone. Find the posterior density of theta = Pr(krone), along with "standard summary numbers", namely posterior mean, posterior standard deviation, 0.05, 0.50, 0.95 posterior quantiles, for each of the following priors:

(a) theta is uniform on (0,1) (which is where Thomas Bayes started, in 1763).

(b) theta is a Beta(c,c), with a high c, like c = 100.

(c) theta is a mixure 0.50 * uniform + 0.50 * Beta(c,c).

(d) the...

On Wed Sep 20 I went through some general aspects of Ch 3, including the Dirichlet-multinomial setup and some of the details for the Gamma-Normal setup for normal data. These matters will be pursued further in the coming lectures. Exercises discussed were (1) setting up alternative priors for the N parameter with the streetcars of San Francisco; (2) applying the normal-normal setup to assess the IQ of an individual given his or her test result; and (3) most of Exam stk 4020 2008 Exercise 2.

For Wed Sep 27, do the rest of the Abel enevelopes exercise of Exam 2008, giving a full posterior distribution for \gamma, the number of 1929 Abel envelopes issued by the Norwegian postal authorities. Then do Nils Exercise 14, before doing as much as you can of Nils Exercise 13. Finally do Nils Exercise 22, with the Gamma-Normal prior, with the cigarette data.

I've uploaded the R script com20a, for Exam 20008 Exercise 2, the co...

As we know, the four-hour exam date is Wed December 13.

*Tentative dates* for the Exam Project is from t_0 = Thu November 30 to t_1 = Mon December 11. Please write til Nils is you have particularly good reasons to not being happy with this time window. The [t_0, t_1] will be made official within Fri September 22.

1. On Wed Sep 13 we went through Exam stk 4021 2015 Exercise #1, and the extended streetcars in San Francisco exercise, with three datapoints y1 = 203, y2 = 157, y3 = 222, rather than only the first. I also pointed to various related issues. Then I rounded off Ch 2, with emphasis on the case of normal model + model prior giving normal posterior. See in this connection exercise (b) below, for next week.

2. I'm placing R scripts com18a (for Exam stk 4021 2015 Exercise #1) and com19b (for SFr streetcars) on the course website. Run them and make sure you understand what goes on.

3. Next week I focus on Ch 3, with multidimensional parameters. The basic concepts carry over from the one-dimensional case, but computational issues are going to be harder.

4. Exercises for Wed Sep 20:
(a) First, to the SFr streetcars one more time, now with *four* datapoints, 203, 157, 222, 314, using variations of my com19b programme, *and* where you construct your own pr...

Check on the site for a note from Emil, produced 7-Sep-2017, essentially using tools & tricks from BDA Ch 2, to predict how well Arbeiderpartiet does on Monday 11-Sep-2017.

1. On Wed Sep 6, Emil Stoltenberg taught in loco Hjorti. He went through most of the appointed exercises, from Ch 2, and also Nils Exercise 12. In connection with these exercises he also discussed basic concepts from BDA3 Ch 2, including the *Jeffreys prior* and prediction.

2. See "Notes from Emil Stoltenberg", with details related to solutions of the Ch 2 exercises.

3. Emil also had time to explain that *just with tools and tricks from Ch 2* one can build good models and methods for election predictions. He will produce a short note on this, with Norwegian data, to be placed on the present course site.

4. Next week I will continue with Ch 2 themes, the use of Jeffreys, the prior and posterior predictive, etc.

5. Exercises for Wed Sep 13: First, 2.16 from the book. Then, extend Exercise 2.10, by computing posterior mean and standard deviation for N, and a 90% credibility interval, for the case of having o...

1. On Wed Aug 30 we went through Nils Exercises 1 and 2, with various pieces of extra commentary and insights, also regarding the Fantastic Master Theorem. I also filled in with more details from Ch 1, and started on Ch 2. One aspect there is the "Nice List", cases where the model and the prior are nice enough to lead to nice and amenable posteriors: (Poisson, gamma), (binomial, beta), (normal, normal), and more.

2. I've placed my (simple and not streamlined) R script "com17a" on the course site, with R code for some of the details of Nils Exercise 1.

3. I'm travelling next week, and my PhD student Emil Stoltenberg will teach in loco Hjorti. I'm hoping that he can use ten minutes of his teaching time to tell you about *predicting the outcome of the election*, using Bayes methods. Check 169.no, where some of our colleagues are producing such prognoses.

4. Exercises for next week: First, Nils Exercise 12; then as far as time permits from the book's 2.1, 2.3,...

1. On Wed Aug 23 I gave a general introduction to the course, discussing also in which basic ways Bayesian statistics differs from classical frequentist (Fisherian) statistics. I also went through the essential practicalities of the course, regarding teaching (most of the time meant to be two hours lecture + one hour exercise, but with modifications), exam, etc.

2. The curriculum will essentially consist of BDA Chapters 1, 2, 3, 4, 5, 9, 10, 11; details will be given later. A classic sentence in curricula for my courses is "also, all exercises we've been through during the course are considered part of the curriculum".

3. The exam will consist of two parts: *The Project*, over approximately ten days, from time t_0 to t_1, where these dates will be decided on by mid September; and a *four-hour written exam*, on Wed December 13.

4. Next week I'll have a few more comments regarding Ch 1 before embarking on Ch 2. I will talk through the details of the "Fantasti...

Welcome to the course! The course book is "Bayesian Data Analysis" (Gelman, Carlin, Stern, Dunson, Vehtari, Rubin, 3rd edition, 2014), which even has its own webpage:

www.stat.columbia.edu/~gelman/book/

You should get hold of a copy, before teaching starts; try Akademika, or eBay, or Amazon, or verdensveven.  Only some of the chapters of the book will be in the main curriculum, and there will also be supplementary notes and exercises; check earlier versions of the course on this website.

Teaching will take place in VB, Auditorium 2, Wednesdays 12:15 to 15:00 (typically in the format of two hours of lecture and then one hour of exercises), and we start off Wednesday August 23.

Nils Lid Hjort