SubjectsSubjects(version: 867)
Course, academic year 2019/2020
Bayesian Methods - NMST431
Title: Bayesovské metody
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2 C+Ex []
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information:
Guarantor: prof. RNDr. Marie Hušková, DrSc.
doc. RNDr. Arnošt Komárek, Ph.D.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Pre-requisite : NMSA407
Annotation -
Last update: T_KPMS (15.05.2013)
Prior and posterior distributions, conjugate families, Bayesian test and estimators, applications.
Aim of the course -
Last update: T_KPMS (15.05.2013)

Basic principles of Bayesian approach to statistical problems

Course completion requirements -
Last update: doc. RNDr. Arnošt Komárek, Ph.D. (12.10.2017)

The course credit for the exercise class will be awarded to the student who hands in a satisfactory solution to each homework assignment by the prescribed deadline.

Literature - Czech
Last update: T_KPMS (15.05.2013)

Hušková M.: Bayesovské metody, UK Praha, skripta, 1985

Pázman, A.: Bayesovská štatistika, UK Bratislava, skripta, 2003.

Robert, C.P.: The Bayesian choice, Springer, 2001.

Teaching methods -
Last update: T_KPMS (15.05.2013)


Requirements to the exam -
Last update: doc. RNDr. Arnošt Komárek, Ph.D. (12.10.2017)

Exam is oral (2 problems assigned at the beginning of exam, student prepares answers on a paper and will consequently present and discuss them with the examiner). Exam will cover topics covered by both lectures and exercise classes.

Syllabus -
Last update: doc. RNDr. Arnošt Komárek, Ph.D. (29.10.2019)

Bayes theorem and its use, prior and posterior distribution, methods to choose a prior distribution.

Statistical decision functions.

Bayes point estimators and their properties. Credible sets.

Bayes hypothesis testing, some special tests.

Some special bayesian approches, basics of MCMC.

Entry requirements -
Last update: doc. RNDr. Arnošt Komárek, Ph.D. (25.05.2018)
  • Probability space, conditional probability, conditional distribution, conditional expectation;
  • Foundations of statistical inference (statistical test, confidence interval, standard error, consistency);
  • Maximum-likelihood theory including asymptotic results;
  • Linear regression (including related theory);
  • Generalized linear models, linear mixed model (at least applied knowledge);
  • Working knowledge of R, a free software environment for statistical computing and graphics (
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