Beskjeder

Good luck to all with the Exam Project. Remember to submit both "Page A" and "Page B" with your report (see the introductory text). Also include clear references if you should happen to need or use material or methods outside the course curriculum. Contact me if there are technical obstacles or practical questions.

We meet Wed Dec 5 for a final "review of the curriculum" opportunity. Students are encouraged to prepare specific questions. The Exam Set will be put up at this website by Fri Dec 7. Reports (preferably text processed) need to be handed in by Mon Dec 17 (more details later).

I have uploaded com25d and com25e, both related to the random telephone numbers of Exercise 16f, with two different implementations of the Gibbs Sampler.

Exercises for Wed Nov 28: 16(f), 18(e), 24, 25, 27, from Exercises, update D.

Note that I have uploaded a pdf version of Petter Abrahamsen's guest lecture on this site.

1. Various new "com" R files have been uploaded to this website, including those related to simulation of Gaussian processes.

2. Wed Nov 21 we all go to Norsk Regnesentral, 12:15 -- 14:15, konferanserom "Delta", where Petter Abrahamsen will give a lecture on simulation related methods in use for oil exploration etc. (This is part of the curriculum for the course.)

An updated and extended version of the Exercises file has been uploaded; please print out the appropriate Exercises, update D, now comprising 30 pages and a total of 32 exercises.

Exercises for Wed Nov 14 are as indicated in the previous message, but since the "Update D" is now available I redefine the homework assignment to be Exercises 18(e), 20, 21, 22, 23.

It is also advisable to read through all remaining exercises, as the course curriculum will include (nearly) all of them.

An updated and extended set of exercises will be placed on this website by Fri Nov 9 evening. Exercises for Wed 14 are: Simulate paths from (a) the Brownian motion process over the unit interval; (b) the Brownian bridge process over the unit interval; (c) the Ornstein--Uhlenbeck process over say [0,10]; (d) the process Y(t) = 0.95 OU(t) + 0.05 W(t) over [0,10]. Evaluate the probability that the maximum of the last process exceeds the threshold 4.444. (More details are provided in the updated and extended set of exercises.)

Wed Nov 7 I will use most of the time to go through the Gibbs Sampler of Chapter 6, with various examples. I will also discuss simulation of Gaussian Random Fields and indicate some of their uses.

Examination in this course takes the form of an exam project, where a set of exercises is made available at this website Friday 7 December, and where each student hands in a written report by Monday 17 December; more details to follow.

I'm at a conference in Oberwolfach next week, and there is no teaching in this course on Wed Oct 24.

I have uploaded com25a and com25b for Exercise 16.

For Halloween day, do all of Exercise 16, including the following point: suppose I have observed 1234 telephone numbers, for which I have computed U(x), with average value 11.111. Estimate the parameter lambda.

Also: implement Metropolis for simulating from the distant bi-mixture 0.5 N(-5,1) + 0.5 N(5,1), where the proposals are of the form xnew = xold + unif(-delta,delta). Which values of delta work well?

Also: do Exercises 14 and 15.

For Wed Oct 17, do Exercises 4, 13, 15, 16, in approximately that order of preference.

I have uploaded com24a for Exercise 12, and Update C for the Nils exercises, now comprising 16 exercises over 11 pages.

We interpret the following general message as implying that there will be regular teaching in our course Wed Oct 10.

"Minner om at neste uke er det midtveiseksamen. Det er derfor undervisnings-fri i alle emner p? bachelorniv? og emner som er klonet (emner som g?r b?de p? bachelorniv? og masterniv?). Emner som kun er p? masterniv? kan g? som normalt."

For Wed Oct 10, do Exercises 12, 4, 9, in approximately that order of preference. That week we also start entering the MCMC world of Chapters 5 and 6.

For Wed Oct 3 I will give a brief guided tour of the topics of Chapters 3 and 4, including a bit on the Dirichlet process for Bayesian nonparametrics (Section 4.4). The plan is to use rather more time for Chapters 5 and 6, starting on these topics Wed Oct 10.

Exercises for Oct 3: Exercise 10(c), 11.

Notate bene: a new and extended version "Exercises, update B" (pdf file) is now uploaded to this site. It has now 12 exercises and comprises 7 pages. I have also placed R commando files "com18a" (for Exercise 3) and "com22a" (for part of Exercise 10) at the site.

For Wed 26.9: work with Nils Exercises 3 and 4, and then tend to the following task: For the g(x,y) integrand function worked with in Nils Exercise 1, define f(x,y) = g(x,y)/I. Draw 10,000 samples from this density, using rejection sampling. Compute means, standard deviations, correlation, and display marginal densities.

For Wed 19.9: work with Exercises 6,7,3 from Nils's stk 4050 (growing) collection, in more or less that order. I will lecture from Liu's Ch 2.

I have placed "R source files" here; please check that you can access, copy, modify, and use them. Keeping "com16b" in the appropriate subdirectory of your computer and then writing the command line " source ("com16b") " inside R will execute this programme, which pertains to Exercise 1. As the course proceeds you will be expected to be able to make such programmes yourself.

For Wed 12.9: work with Exercises 1,2,3,4 from Nils's stk 4050 (growing) collection. We are otherwise still at the "introductory part" of the course. Next week again we shall proceed to attack Chapter 2 i Lui's book.

Da jeg arbeider i Belgia onsdag 29.8 starter undervisningen uken etter, alts? onsdag 5.9. Det er klokt om alle f?r tak i et eksemplar av Lius bok. Jeg kommer til ? snakke summarisk om Ch 1 f?r jeg g?r inn i diverse detaljer i Ch 2.

1. Det blir ingen undervisning onsdag 22.8, siden jeg arbeider i Cambridge den uken.

2. Pensum i kurset vil delvis bygge p? boken "Monte Carlo Strategies in Scientific Computing" (2001, Springer Verlag), av Jun S. Liu, og delvis p? artikler som vil bli delt ut gjennom kursets gang.

Nils Lid Hjort