# Elementary Bayesian Analysis, fall 2008

### Lecturer

Lecturer: Academy Research Fellow, Doc. Aki Vehtari <aki vehtari at tkk fi>

Assistant: Jukka Sirén <jukka p siren at helsinki fi>

### Scope

9 op

### Type

Intermediate studies.

### News

Summer exam 11.06.2009 or 13.08.2009

### Lectures

Period II, Wednesday 12-16 in room D123 (Exactum, Kumpulan kampus). First lecture 29.10.2008.

- Lecture 1 - Introduction (Ch 1)
- Lecture 2 - Single parameter models (Ch 2)
- Lecture 3 - Multi-parameter models (Ch 3) , Large-sample inference and frequency properties (Ch 4)
- Lecture 4 - Hierarchical models (Ch 5), Introduction to computation (Ch 10+11)
- Lecture 5 - Computation (Ch 11+13), relevant pages on Geyer's estimates
- Lecture 6 - Decision analysis (Ch 22), Model checking and improvement (Ch 6)
- Lecture 7 - Modeling accounting for data collection (Ch 7), Connections and challenges + General advice (Ch 8+9), Some example applications

**Prerequisites**

Basics in statistical mathematics and probability calculus.

### Register

Registration is closed.

### General info

Main literature is the Gelman, Carlin, Stern & Rubin: Bayesian Data Analysis, Second edition. Course will cover the chapters 1-14 and 22 with varying depth. This book is essential in the course and very useful also later if you are going to apply Bayesian methods. Some additional reading will be listed below.

Cheapeast way to buy a new copy of the book, seems to be ordering directly from the publisher (CRC Press) 37£ (~46e) with free shipping to Finland.

### Requirements

To pass the course you need to get 50% of maximum points in each sub-part: 1) exam, 2) pen and paper exercises, and 3) computer exercises. If you pass all three sub-parts, the final grade is determined based on average of normalized points. Note that, to pass the course more than half of the exercises have to be made correctly, ie. to pass the course you don't need to return all exercises, but if you want to learn, it is highly recommended.

### Exam

Exam is 16.12. 12-16 in Exactum A111 or B123. Please register in advance. Registration is open 14.11.-8.12.2008. All exam questions are based only on the material in the course book.

- Example exam questions(example questions have been updated 9.12.2008)

**2nd exam** is 22.1. 16-20 in Exactum A111 or B123. You may take the exam, even if you have not registered!

### Pen and paper exercises

Pen and paper exercises are

- 1.1,1.2,1.3,1.4,1.6,1.7,1.8
- 2.1,2.2,2.3,2.4,2.7,2.8,2.10,2.12,2.14
- 3.1,3.9,3.13
- 4.4
- 5.2,5.3,5.5,5.8,5.10
- 6.5,6.6,6.11
- 7.1,7.2,7.3,7.5,7.6
- 8.8,8.9
- 10.1
- 11.1,11.2
- 22.1

Deadline for returning these is 15th December 2008. If you miss the first deadline, a second deadline is 1st of February 2009. Since many of these exercises are easier to write with pen instead of computer, you may return these in paper form to lecturer or assistant (at lecture class, computer lab, or mail room C334). It is recommended to try to do exercises related to week's lecture before the next lecture (but return all answers at once). Try to make these on your own, but you are allowed to discuss them with other students.

### Computer exercises

Instructions for the computer excercises are below in pdf. Instructions and excercise templates assume the use of Matlab (installed, e.g, in Exactum C128) but you may use other software like R, too.

Write an exercise report for the computer exercises (except 1.9). Describe your solution briefly, show the code you have used, and describe and discuss your results. You will get 0-5 points for the results and additional 0-1 points for meaningful discussion (as long as there are some results). In the discussion part you may comment if something was unclear or what questions or ideas did this exercise raise. You may also discuss the relevance of the exercise for this course. Note that appearance of the report is not important as long as the report is clear. Use of report template given is optional.

- Report instructions
- Report template pdf (optional)
- Report template tex (optional)
- Matlab code templates (just fill your answer)
- Useful Matlab functions for making exercises
- Demonstration (esim) files

Deadline for returning these is 15th December 2008. If you miss the first deadline, a second deadline is 1st of February 2009 . Since you need to return some code, and figures, it is easier if you make electronic document with your favorite document writing program and email the report to the assistant <jukka p siren at helsinki fi>.

Assistant Jukka Siren will help with the computer exercises at computer lab Exactum C128 at thursdays 10-12.

Computer exercises can be made in pairs (and with permission from lectured in groups of three). Return one report including names of all students in a pair (or a group). Note that you should co-operate on all exercises and all of you should understand all answers you return.

### Additional reading

O'Hagan describes two types of uncertainty in his articles Dicing with the unknown and Simulation and uncertainty, which are useful in making the difference between the uncertainty described by the statistical model and the uncertainty associated to the parameters of the model in question. This issue will be discussed more throughly in the first lecture.