Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Statistics and Social statistics module.

Bachelor studies in mathematics and statistics or equivalent knowledge.

It is assumed that you have taken at least one of the following courses:

MAT22005 Bayesian inference

DATA11006 Statistical Data Science

LSI35002 Bayesian data analysis

or a course covering basics in Bayesian inference.

MAST32001 Computational statistics

MAST32005 Spatial modelling and Bayesian inference

The course covers some foundations of Bayesian statistics and its theoretical links to decision theory. After the course you will understand the justification and axiomatic construction for probability as a measure of subjective uncertainty and how this leads to Bayes theorem. You will also be introduced to properties of Bayesian inference in the limit of large data and to De'Finetti's Theorem and their basic consequences and interpretations. After the course you will understand what are model's marginal likelihood and Bayes factors, posterior predictive model comparison and validation, decision analysis and experimental design. You will also be able to apply these techniques to practical data analysis tasks.

Week 1. Revisal of basics and robust regression Week 2: Model's marginal likelihood and Bayesian inference in the limit of large data Week 3: Probability as a measure of uncertainty and Decision theory Week 4: Score functions and model comparison Week 5: Model comparison and selection with cross validation and information criteria Week 6-7: Design of experiments

Lecture notes, Chosen sections from the Bayesian data analysis book, and articles to be announced during the course

Lectures, exercises and exercise groups

Exam. Course will be graded with grades 1-5. Exercises provide extra points to the exam.

Nykyisestä koronavirustilanteesta johtuen salitentit on peruttu. Voit olla yhteydessä tentaattoriin korvaavan suoritustavan sopimiseksi.

Exam