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Thanks for your efforts with the Exam Project. The follow-up oral examination part, with perhaps 20-25 minutes per candidate, is organised as follows, Thu Dec 19, in Room 1020 (Abel Building, tenth floor): 

 9:00 Dennis Christensen 
 9:30 William Denault 
10:00 Maria Nareklishvili
10:30 Leiv Tore Rønneberg 
11:00 Marthe Elisabeth Aastveit 

Nils Lid Hjort & Anders Løland

1. The Exam Project will be made available on this course site, Wed Dec 4th, morning, and reports need to be handed in by Mon Dec 16th, at 10:59 or earlier; instructions are given on page 1 in the project description. Importantly, each report needs to contain *two extra special pages*: (i) a signed self-declaration form, essentially saying "I have worked on this by myself, and have duly referenced things & thangs I might have found in the libraries in the world, and I am not a plagiarist (etc.)"; and (ii) the student's one-page summary of the exam project, also containing a brief self-assessment of its quality. So if you feel that you've earned a clear A, say it (etc.).

2. Then on Thu Dec 19th there will be 25-minute oral examinations of the candidates; precise information about time schedule etc. will come in due time.

Good luck with your efforts!

I'm anderswo engagiert, on Tue Nov 5, but Gudmund Hermansen will teach, or perhaps rather give a mini-lecture, 9:15 to 11, with interruprtions and details, regarding a joint project of ours (which ought to be finished): Bayesian Nonparametrics for stationary Guassian time series. This is the thing: if y_1, y_2, ... are from such a time series, then there's a well-defined correlation function, which by the right theorem can be represented as

\corr(y_i, y_j) = 2 \int_0^\pi \cos( |j-i| \pi\omega)\,{{\rm d}}F(\omega,

for a suitable probability measure F on [0, \pi]. We may then put a Dirichlet process on this F, e.g. cented at the appropriate F_0 for an autoregressive process of some order, etc.

Thanks to Dennis Christensen for his 30-minute contribution last week; next week, Tue Nov 12, we're having

Maria Nareklishvili: Instrumental Variable Regression and its applications, Bayesian approach

The "Beta Processes for Roman Era Egypt" themes today caused me to make a few comments about the intriguing dynamic plot shown in the link below: 

Wahrlich, wir leben in ... interessanten Zeiten, with gigantic & fundamental changes in demography and medicine, under our feet. Over as short a time-span as a brief century, two fundamental parameters, Pr(a child dies before age five) and E (number of children), have gone down, super-significantly and super-uniformly.
https://www.facebook.com/groups/1589206911336271/permalink/2347692038821084/
 

The Department and the Faculty wish to see that when we give a course, for both Master's and PhD level candidates, then there ought to be a "visible difference" in the ways the exams are designed. One solution is to give 4 exercises to the Master students but 44 such for the PhD students, for the exam project in December. For this occasion I choose another solution, however, for our *four PhD candidates*, namely that they give us *30 minute talks*, on topics touching their own research work, and sufficiently close to our course topics, as part of the regular teaching. 

This is our schedule, so far, and soon we will have *titles and short abstracts* for all of these:

Tue Oct 29: Dennis Christensen: Applications of Bayesian linear regression in sensitivity analysis of energetic materials

Tue Nov 12: Maria Nareklishvili: Instrumental Variable Regression and its applications, Bayesian approach

Tue Nov 19: Leiv Tore Salte Rønneberg,...

1. Wed October 14 was a "theory day", where we went through various basic issues regarding first the time-discrete and then the time-continuous Beta processes, with priors, posteriors, etc. 

Note that *exam dates* are now determined; check the relevant message concerning this, with a bit more details to follow soon.

2. Wed October 21 will be "practical day", where we go through several exercises. 

(a) Do Nils Exercise 28, concerning lifelengths for brave Roman Era Egyptian men and women, a century B.C. Use Beta processes, with prior mean function A_0(t) corresponding to a Gamma distribution with mean 30.00 and standard deviation 20.00, and take prior certainty function c(s) = 10/\sqrt(1 + s), on the time scale of years. Draw sim = 100 curves from the posterior processes the cumulative hazard functions A(t), for men and for women, and for the survival functions S(t), for men and for women. Invent your quantity to examine, to address the question of...

First, the Exam Project will take place for the time window [t_1, t_2], where the exam set will be made available on the course site at t_1 = Wednesday December 4, at noon, and project reports need to be handed in to The System within t_2 = Monday December 16, at 12:59 Blindern time. Details regarding this, whether a pdf needs to be uploaded to a system, or whether Nils rather wishes to have two copies delivered to him, will be made clear a little bit later. 

Second, there will be a 25 minute per candidate oral examination, some candidates on Wednesday December 18, some on Thursday December 19. Again, details will come regarding this a bit later. 

1. On Tue Oct 8 I discussed aspects of Bayesian and classic frequentist bootstrapping, and illustrated this in the case of dtaa from an exponential distribution, with the task being to produce confidence intervals for each of \xi = mean, \sigma = standard deviation, \gamma = skewness. See com45a, the relevant Nils R script.

2. I also went through the basics of convergence of random processes on the space D[0, 1], of all right-continuous functions with left-hand limits, x:[0, 1] to R, with the Skorohod metric. Construction of various processes can be put up along the lines of Interesting Process = limit of simpler processes. Among these are Brownian Motion and the Gamma processes; see Exercises 20, 21, 22, 23, 24.

3. For Oct 8, do the following, an application of the Gamma process + Poisson process setup. (a) Consider a Gamma process Z(t) on [0, 1], with Z(t) being Gamma( b A(t), b), with A(t) the integral of a(s) = 10 + 0.75 \cos(2\pi s). Draw 25 samples of Z...

For Tue Oct 1, I will discuss the Dirichlet processes further, including their application to clustering processes, and then go on to Gamma-Poisson processes, see Lecture Notes Exercises 20, 21, 22, 23, 24.

For exercises: First, do the following. Generate  a dataset of size n = 50, from the unit exponential model. Consider the three parameters \xi = the mean, \sigma = the standard deviation, \gamma = the skewness (without "knowing" that the data are exponential). (a) Estimate the parameters. (b) Carry out Efron classical bootstrap, to assess their uncertainty. (c) Carry out Bayesian bootstrapping, to do the same. (d) Compare.

Then: do Nils Exercises 20, 21A, 21B, 22, 23.

I'm doing panel work for the European Research Council in Bruxelles most of the week Sep 23-27, so there'll be no teaching on Tue Sep 24. As I mentioned I had hoped that Gudmund Hermansen could step in for two hours, to go through his and my work on Bayesian Nonparametrics for stationary time series, involving placing a Dirichlet process prior on the spectral distribution, etc. He is being anderswo engagiert, however, and will visit out course later on in this semester.

A little bit later I'll give you exercises to go through for Tue Oct 1, so check this course website. One of these will be as follows: I give you an iid dataset; then you carry out (a) classic Efron nonparametric bootstrapping for inference about the mean, the standard deviation, the skewness; and (b) different and less familiar Bayesian bootstrapping, for the same quantities. Again, details will come.

1. On Tue Sep 10 we went into various aspects of the Dirichlet process, regarding construction, existence, interpretation, simulation ("brute force" via lots of boxes, and also stick-breaking), prior to posterior updating. We also discussed bits & pieces of Exercises 4, 5, 6, 7, 8.

2. I've uploaded R scripts com43a (for Gott würfelt nicht, kann es der wahre Jacob sein?) and com44a (for the Nils VIE Very Important Exercise 8, with simulations for prior and posterior Dirichlet processes). Copy them, use them, check their steps, play with other parameter values, etc., and be able to modify them.

3. Next week we do more on the Dirichlet processes, including also modelling setups where the Dirichlet process generate parameters, as opposed to generating data directly.

4. Exercises for Tue Sep 17: First do the following simple extra exercise. y is binomial (n, \theta), and \theta has the interesting prior 0.50*uniform + 0.50*\delta(0.50), the second compone...

1. On Tue Sep 3 I went through more on the multivariate normal and on Gaussian processes, where Nils Exercise 40 fits in as Bayesian nonparametric machine for spatial interpolation, along with uncertainty assessment. I also commented more on what is now Exercise 2B, with different loss functions.

Then I went through aspects of Exercises 5, 6, 7, leading up to the famous Dirichlet Process, with a definition for P being a Dir(a P_0), etc. We'll do more on this over the coming few weeks. 

2. Exercises for Tue Sep 10: First, do the extension (d) of Exercise 2B, inventing your own loss function with three possible actions: \{do nothing, ask for more data, change the system\}. Then do Exercises 4, 7, 8. For the latter, simulate DIrichlet processes via "brute force on a tiny grid".

I've uploaded an updated version of the Nils Collection, now comprising 51 pages, and called version 0.77. It has Exercise 2B, which we more or less did last week (two binomials, two loss functions); a new Exercise 21A (with Gamma and Poisson processes); a new Exercise 39A (on the multivariate normal, with conditioning properties and simulation); and more details in Exercise 40 (Bayesian Kriging, which can be seen as Bayesian nonparametrics for spatial interpolation and uncertainty assessment).

Check out the Exam Project Spring 2018, for the skiing days at Bjørnholt exercise. We'll do that one in a little while.

1. On Tue Aug 27 I worked through Exercises 1, Nils Extra 1, and the essence of Exercise 40. I also talked about the basics of Gaussian processes used as priors for unknown functions, when these are e.g. observed a finite number of locations. I also went through parts of the Nils Big Insight Feb 2017 talk (with the pdf available at this site).

2. I've uploaded Nils R scripts com41a (for Exercise 40) and com42a (for Nils Extra, two binomials with two loss functions). Run them, with variations, to make sure you know what goes on at each step. 

3. For Tue Sep 3, go through *more of Exercise 40*, including generating m(x) curves from the prior and the posterior. Then do Nils Exercises 3 and 4. Also, *look through* (without necessarily doing all of it) Nils Exercise 5 (the Dirichlet Process), and the Exam Project 2018 Exercise 2. We will return to details later.

1. Today, Tue Sep 20, we started the course!, and I gave a broad general introduction to the course & its themes. Again, the core currilcum will use (i) the Müller at al. book, Springer, 2005; (ii) the Nils intro chapter from "Bayesian Nonparametrics" (Hjort, Holmes, Müller, Walker, the 2010 Cambridge book); (iii) various things from the "Nils Collection" of Exercises and Lecture Notes.

2. Note that I've placed the Nils Collection and the Nils intro chapter at the course website, where there also will be other material in due course. In a week or two I plan also to go somewhat briefly through the BigInsight talk (2017) which is also placed there.

3. Exercises for Tue Sep 27 are as follows. First, as an extra exercise, assume y_0 is binomial (n_0, p_0) and y_1 is binomial (n_1, p_1), with y_0 = 33, y_1 = 44, from sample sizes n_0 = 100 and n_1 = 100. For priors, take p_0 and p_1 both uniform. (a) Give the Bayesian point estimate for \delta = p_1 -...

When I gave the course in the spring semester of 2018 I wrote up 47 pages of Exercises and Lecture Notes. I've now placed a mildly edited version, dated 19-Aug-2019, at the course website -- print out a copy for your convenience. Many of the exercises for the course will be taken from these. 

Later on in the course I'll include a few more exercises, including almost-worked-out applications, and then place updated versions of this collection on the site.

I look forward to giving the Bayesian Nonparametrics course. The teaching sessions take place in room 819 (8th floor, Abel Building), Tuesdays 9:15 to 12:00, and we start 20th of August. For most of these Tuesdays I intend to use the basic formula two hours teaching + one hour exercises (where one hour is a Blindern teaching hour, i.e. 45 minutes).

You ought to to check out the course website for STK 9190, spring semester 2018, with messages, exercise collection, and the Exam Project.

There are several books on Bayesian Nonparametrics, including Hjort, Holmes, Müller, Walker (Cambridge, 2010), where its introductory chapter will be part of the curriculum. The main course material will however be from Müller, Quintana, Jara, Hanson (Springer, 2015), "Bayesian Nonparametric Data Analysis". Please get hold of your own copy, perhaps via Amazon or eBay -- and I do think it's freely available as a pdf from the web via the Department...