M9211 Bayesian methods

Faculty of Science
Spring 2020
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
Mgr. Ondřej Pokora, Ph.D. (lecturer)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 10:00–11:50 M1,01017
  • Timetable of Seminar Groups:
M9211/01: Mon 14:00–15:50 MP1,01014, O. Pokora
Prerequisites
Students are supposed to have theoretical knowledge as well as practical experience in the topics of basic courses of Probability and mathematical statistics and Calculus. The experience in working with software environment R is supposed, too.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This course introduces the basic principles and methods of the Bayesian statistics. The student learns the theoretical principles of these methods and the techniques for calculation of the estimators and their application in inference and prediction. The course also deals with the basics of information theory and with the numerical and simulation methods of the calculations. In the practical classes, the student learns how to calculate the aposterior density and the Bayesian estimators in real problems, how to interpret them and how to compare them with the classical statistical estimators. Further, the student goes through the computer implementation of the methods of numerical integration and Markov-Chain-Monte-Carlo simulations.
Learning outcomes
After completing this course, the student will be able to:
- understand the methods of the Bayesian statistics and to interpret their parameters;
- calculate the Bayesian estimators and to infer in real problems;
- compare the Bayesian and the frequentist approach;
- evaluate the aposterior density by approximations and by the Markov-Chain-Monte-Carlo methods using computers;
- evaluate the I-divergence and the information gained from the experiment.
Syllabus
  • Bayes' theorem and aposterior probability density.
  • Bayes' formula for discrete and continuous random variables.
  • Chain rule.
  • I-divergence and information gained from the experiment.
  • Entropy and mutual information.
  • Noninformative priors.
  • Computational methods for evaluation of the aposterior probability density.
  • Conjugate systems of the prior probability densities.
  • Simulation methods, Monte-Carlo integration.
  • Markov-Chain-Monte-Carlo methods.
  • Calculation of the Bayesian (point and interval) estimation, inference and prediction.
Literature
  • GELMAN, Andrew. Bayesian data analysis. 2nd ed. Boca Raton, Fla.: Chapman & Hall/CRC, 2004, xxv, 668. ISBN 158488388X. info
  • DAVISON, A. C. Statistical models. 1st pub. Cambridge: Cambridge University Press, 2003, x, 726. ISBN 9780521773393. info
  • PÁZMAN, Andrej. Bayesovská štatistika (Bayesian statistics). Bratislava: Univerzita Komenského Bratislava, 2003, 100 pp. ISBN 80-223-1821-3. info
  • HUŠKOVÁ, Marie. Bayesovské metody (Bayesian methods). Praha: Univerzita Karlova v Praze, 1985, 93 pp. info
Teaching methods
Lectures: 2 hours a week.
Exercises: 2 hours a week, work with mathematical software R, homeworks and individual project.
Assessment methods
Exercises: active participation, homeworks and individual project.
Final exam: practical (on PC), written and oral part. At least 50 % of points in total is needed to pass.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms spring 2018, Spring 2019, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2020, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2020/M9211