# Messages

Thanks to all candidates for their work & efforts regarding The Project, alias the Exam, Part I. Now for the Exam, Part II, four hours, Mon December 17th, 14:30 to 18:30, in Gymsal 4, Idrettsbygningen. You should bring along **one simple-style calculator** (i.e. without heavy memory capacity etc.) for just a few simple calculations to be carried out; **also** as previously explained you are allowed to take along **precisely one page** of handwritten preparation notes, prepared by yourself. Good luck!, and thanks a priori and a posteriori for your efforts.

We expect the results of the exam to be made available to the central StudentWeb registry by Fri December 28.

**Important:** For the four-hour written Exam Part II Mon Dec 17, please bring with you (a) an ordinary pocket calculator and (b) **exactly one page** of **handwritten preparation notes**, prepared by yourself as you wish with whatever you feel might be useful for for the exam. You may write as tinily as you wish, but for this Exam Part II you are not allowed to use the course book or any other material.

For an example of how such an exam set may look like, check the 2006 exam set under http://www.uio.no/studier/emner/matnat/math/STK4020/oppgaver/

**Important:** I have now uploaded Andrew Gelman's 2008 article "Objections to Bayesian Statistics" to this course website, taken from the "Bayesian Analysis" online journal, along with discussion contributions by Jose Bernardo, Jay Kadane, Stephen Senn, Larry Wasserman, and Gelman's rejoinder (Gelman is himself a prominent Bayesian, but chose nevertheless to air some of his objections to Bayesian practice in this manner). All students may benefit from sifting through these, but this particular message is primarily directed to **the PhD students who are taking the STK 9020 version** of the exam. **All students** shall work with Exercise 1, 2, 3 from the Exam Set 3-Dec to 14-Dec, but **the PhD students** are also required to work on **Exercise 4**.

This last Exercise 4 is as follows: Read through the Gelman 2008 paper and ensuing discussion, and **write up a short essay** (perhaps three pages?) where you...

1. Note that I have uploaded com15a and com16a (MCMC scripts for Exercise #21) and com26a (re Exam stk 4020 2004, #4, inference for an ensemble of binomial parameters).

2. We have essentially finished Ch 5 and next week I'll go through a coupl' o' stories from Ch 7; see also the **pensumliste** (curriculum list).

3. Exercises for Wed 21: We have just a few more points to go through regarding Exam stk 4020 2004 #4 (you may use com26a, now available, as a basis for these remaining points). Then Exam stk 4020 2004 #2 and #3 (as far as time permits).

1. Note that I have uploaded "version C" of the **Nils Exercises and Lecture Notes 2012**; print it out for your convenience. It now comprises 25 exercises on 34 pages.

2. **The curriculum** is as follows. From B.P. Carlin and T.A. Louis, "Bayesian Methods for Data Analysis" (3rd Edition, 2009):

Ch 1: All.

Ch 2: Sections 2.1, 2.2, 2.3, then 2.4.1.

Ch 3: Sections 3.1, 3.2, 3.3, then 3.4.1-3.4.2.

Ch 4: Section 4.1.

Ch 5: Sections 5.1, 5.2, 5.6, 5.7.

Ch 7: Sections 7.1.1 and 7.3 are "cursory curriculum".

Appendix B.1.

All exercises discussed during the course are also to be considered part of the curriculum, including earlier exam projects; cf. also Nils Lid Hjort's "Exercises and Lecture Notes" (version C). Note also that some exercises may be seen as `alternative versions' of some of the material in the book; this is e.g. the case for Exercises 22-23 for the inverse-gamma-normal type calculus and Exercises 24-25 vis-a...

1. On Wed Oct 31 we discussed various parts of Ch 5, including empirical Bayes constructions for the "normal-normal" setup, with emphasis also on risk functions for different procedures. For Wed Nov 7 I plan to round off Ch 5, and to discuss "Stein estimation" issues.

2. Exercises for Wed Oct 31: First the few details that still remain for the Egyptian pre-Christ lifetimes, Exam stk 4020 2008 #3. Then Exam stk 4020 2004, #1 and #4.

1. Today we started Ch 5 and went through various details regarding empirical Bayes, specifically for the model that involves binomial data for similar probability parameters and a Beta distribution model for these. We continue Ch 5 next week.

2. Exercises for Wed Oct 31: The rest of the Egyptian life times, Exam stk 4020 2008 #3. Then #1 from the same set. Finally start also Exam stk 4020 2004 #1.

1. Wed Oct 17 we went through the designated exercises, apart from the last points of Exam #2 stk 4020 from 2008, related to the Abel 1929 envelopes. We finish these points on Wed Oct 24, and also work through Exam #3 about lifelengths in ancient Egypt.

2. I somewhat briefly went through Section 4.1. The other sections of Ch 3 are "cursory curriculum", i.e. not in the "active curriculum" part of the course. I also started discussing the empirical Bayes paradigm which is the topic of Ch 5, and shall continue with Sections 5.1, 5.2 next week.

3. I am placing a few "com" R files on the website in the course of this week.

1. Today we went through Nils Exercises 21, 14, and Exam 2010 Exercises 1, 2. We also discussed general MCMC issues.

2. Exercises for Wed Oct 17: The final two points of Exam 2010 Exercise 2; the Abel stamp Exercise 2 of Exam 2008; and then the following addendum to the Gott würfelt nicht exercise Nils #14: Find the posterior distributions of the four parameters rho, alpha, beta, gamma given there, when the prior used for (p1, ..., p6) is an equal mixture between pefectness (the p vector is really (1/6, ..., 1/6)) and the flat Dirichlet (1,1,1,1,1,1).

3. I intend to go somewhat quickly through Ch 4, Section 1 (and the other sections of Ch 4 are not in the curriculum list) and to start on Ch 5.

4. A few R scripts will be uploaded to the course page shortly. These relate to exercises we've recently been through, in particular MCMC constructions.

1. Please note that I have placed **an updated Version B** (dated 4/x/12) of the Nils Exercises & Lecture Notes on the webpage. Print it out for your convenience.

2. Exercises to work through for Wed 10 Oct: Nils 2012 collection #21, #14 (in that order), then Exam Project 2010 for stk 4020 (which you find on the stk 4020 page for that year), #1, #2.

3. Today I summarised most of the relevant material from Ch 3 (where Sections 1, 2, 3, but only 4.1 and 4.2 from Section 4, define the curriculum). We shall however be spending some further efforts on this material when going through exercises. Note also **Nils 2012 Exercises 15, 16, 17** which are to be seen as integrated with the course curriculum version of the book's Ch 3.

4. After a bit more time on Ch 3 material I plan to go through Ch 4, Section 1 on Wed 10 Oct. The other sections of Ch 4 are not included in the curriculum. After Ch 4.1 we start on the important Ch 5.

**Exam, Part II** takes place **Mon Dec 17**, 14:30 to 18:30. **Exam, Part I**, alias "the project", is a set of exercises which will be made available **Mon Dec 3** and for which reports will be handed in by deadline **Fri Dec 14** by 11:59 at the latest.

Note that I have placed "(Further) Nils Exercises & Lecture Notes, 2012" (version A) on the page (there might be a "version B" down the road). Please print out & start reading. Note Exercises 13, 14, which are "inside our curriculum" and my take on the Dirichlet-multinomial model. We shall in particular do Exercise 14 when I'm back from USA and England.

1. On Wed Sep 12 we in essence rounded off Ch 2, though a few details still remain, including Jeffreys prior (pp. 39, 99), which we shall have occasion to work with and use later. We also went through Nils Exercises 15, 13/2008.

2. Nils is in USA Sep 19 (at a university older than USA) and in England Sep 26. There will be no teaching on Wed Sep 19, but **Geir Storvik** will be my stand-in for Wed Sep 26. He will lecture on topics of Ch 3 (details to be provided in a little while), and also go through Exercises 2.19, 2.20(a) from the book. For 2.20(a), invent your own informative prior from the Gamma-Normal family, and if convenient use variations of the R script "com10a".

3. I plan to round off our going through of Ch 3 on Wed 3 Oct. From Ch 3, Sections 1, 2, 3 are curriculum, along with subsections 3.4.1, 3.4.2 from Section 4.

1. On Wed Sep 5 we went through parts of Ch 2, Sections 1-2-3. Material from these three sections will be summarised and rounded off Wed Sep 12, and after that we start on Ch 3.

The curriculum list will have Sections 1-2-3 plus 4.1 from Ch 2 and Sections 1-2-3 plus 4.1 and 4.2 from Ch 3.

2. I also spent a bit of time Wed Sep 5 on the Dirichlet-multinomial model; some of this will be summarised in the form of a couple of exercises in proper "Exercises and Lecture Notes 2012" which will soon be put up on the course webpage.

3. Exercises for Wed Sep 12: From Nils Exercises 2008: 15; then 13, where the emphasis is on points (f)-(g), i.e. it is more important to be able to use the results of earlier points than to go through all required details of points (a)-(e) (but try to, nevertheless); then 2.20 from Ch 2.

1. I have used Wed Aug 22 and Wed Aug 29 to provide a broad, general introduction to the course and its themes. I have touched Ch 1 somewhat indirectly and have started on Ch 2, Sections 1-2-3, which is also our focus Wed Sep 5. Please read through Ch 1, though we will not take time to go through its sections in much detail.

On Wed 29 we also went through Exercises 1-2/2010 and 6-7-8 of Ch 1, along with various connections and side issues.

2. Exercises for Wed Sep 5: First: Suppose y is binomial (n, theta), that the action space is (alarm, no alarm), and that the loss function is as follows: L(theta, no alarm) is 5000 kr if theta > 0.15 and 0 if theta < 0.15, and L(theta, alarm) is 0 if theta > 0.15 and 1000 kr if theta < 0.15. Work out when the correct decision is "alarm", in terms of the posterior distribution, having started with a given prior p(theta). In particular, for n = 50 and with a uniform prior, for which values of y should one decide...

1. Previously I wrote: "Again, find & print out "Nils Exercises" as well as the Exam project set from 2008" -- but I should also have mentioned the Nils Exercises and Lecture Notes (go to "Version C") and the Exam project set from 2010.

2. Exercises, to be worked through by and then discussed on Wed Aug 29: Nils Exercises 2010, #1, 2; the book's Chapter 1, #6, 7, 8.

A tentative description of the part of the curriculum which is based on Carlin & Louis is as follows: Chapters 1 (most), 2 (most), 3 (but only part of Section 4), 4 (only 4.1), 5 (Sections 1, 2, 5), 7 (parts), 8 (parts).

Again, find & print out "Nils Exercises" as well as the Exam project set from 2008.

My lectures will be based on B. Carlin & T. Louis, "Bayesian Methods for Data Analysis" (Third Edition, 2008): http://www.crcpress.com/product/isbn/9781584886976 It has either already arrived or is in the process of arriving at the Academica bookstore. There will also be various extra exercises which I of course will prepare in the course of the course. Please also print out & look through the Exercises collection and the Exam Project set from 2008.

Note that the lectures take place in room B63 in the Abel Building, Wednesdays from 12:15 to 15:00. The course starts Wednesday August 22.

Nils Lid Hjort