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S-114.600 Introduction to Bayesian Modeling

Fall 2003 (2 cr)

27+27 (2+2) f
Teachers: Dr.Tech. Aki Vehtari, M.Sc. Toni Tamminen
Contents: Bayesian probability theory and Bayesian inference. Bayesian models and their analysis. Computational methods, Markov chain Monte Carlo.
Requirements:Exam and exercises.
Literature: Gelman, Carlin, Stern & Rubin: Bayesian Data Analysis, Second edition, and other material announced on course web page.
Prerequisites: First year mathematics are recommended.
Lectures: Mondays 12-14, room E111, in Finnish.
Computer exercises: Tuesdays 14-16, computer lab F402
E111 and F402 are in the Electrical and Communications Engineering building, Otakaari 5.
Exam: 9.12.2003 9-12 hall S4



Lectures are in Finnish, but it is possible to take this course in English by self studying the relevant parts of the book. Instruction in computer exercises is given mainly in Finnish, but it is possible to get some personal instruction in English. The assistant in the computer exercises is MSc Toni Tamminen.

Here is the list of chapters and pages studied in this course. For each chapter there is also a list of exercises. The assistant will help with these exercises in the computer lab. Some of the exercises are marked with *. The assistant will also help with these exercises in the computer lab, but you need to write a report with your solution, results and discussion. More details below.

  1. Background, Ch 1: 3-27, Ex: 1, 2, 4, 6, 7.
  2. Single-parameter models 1, Ch 2: 33-45, Ex: 1, 2, 3, 4, 9.
  3. Single-parameter models 2, Ch 2: 46-55, 61-65, Ex: 8, 11*, 18.
  4. Introduction to multiparameter models, Ch 3: 73-94, Ex: 2, 3*, 4*, 6.
  5. Large-sample inference and frequency properties of Bayesian inference , Ch 4: 101-112, Ex: 1*
  6. Hierarchical models, Ch 5: 117-127, 131-150, Ex: 1*, 2, 6
  7. Introduction to computation, Ch 10, 11, 12: 275-282, 283-308, 311-312, Ex: 10.1, 11.3*, Metropolis and Gibbs sampling**, BUGS*
  8. Decision analysis, Ch 22: 541-544, 552-555, 567-568, Ex 1*
  9. Model checking and improvement, 6: 157-189, Ex: 1*, 7, speed of light
  10. Modeling accounting for data collection, Ch 7: 197-237, Ex: 1
There is a hint page for some of the exercises.


Final grade of the course is the average of the exam and the exercise report provided that you pass (get a '1') both of them.


You are allowed to take one A4 page of notes with you to the exam. You may write anything you think might be helpful as long as you have only one A4 paper. This way you don't need to try to remember everything but instead can spend more time learning and understanding things.

Because there is quite lot of text in course book, here is a more detailed list of things which are required in exam. Exam hints.

Exercise report

You need to write an exercise report for the exercises marked with *. Describe your solution briefly, show the code you have used, and describe and discuss your results. You will get 1 point for the results and additional 1 point for meaningful discussion. In discussion you may write about which parts were unclear or what questions or ideas did this exercise raise. You may also discuss the relevance of the exercise for this course.

The maximum number of points is 11x2=22, and the grade of the report is decided based on following: 12-13=1, 14-15=2, 16-17=3, 18-19=4, 20-22=5. This means that you don't need to solve all the *-exercises to pass the course.

Deadline of this report is 25.11.

You are allowed to write the report in groups of two or three. Return just one report with the names of all students in the group.

Post-graduate students

S-114.600 Introduction to Bayesian Modeling is not considered a post-graduate course. In Fall 2003 post-graduate students may take the course with the code Post-graduate students will get 2 credits.


Bayes, 1763: An Essay Towards Solving a Problem in the Doctrine of Chances (Reprint available at JSTOR)
Stigler, 1986: Thomas Bayes's Bayesian Inference (Available at JSTOR)

You may send your comments to the lecturer

Aki Vehtari
Helsinki University of Technology
Lab. of Computational Engineering
P.O.Box 9203, 02015 HUT
tel: 451 4849

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This page has been updated 5.12.2003