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Course, academic year 2022/2023
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Markov Chain Monte Carlo Methods - NMTP539
Title: Metody Markov Chain Monte Carlo
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: RNDr. Michaela Prokešová, Ph.D.
Class: Pravděp. a statistika, ekonometrie a fin. mat.
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Is interchangeable with: NSTP139
Annotation -
Last update: T_KPMS (19.04.2016)
Markov chains with general state space, geometric ergodicity. Gibbs sampler, Metropolis-Hastings algorithm, properties and applications.
Aim of the course -
Last update: T_KPMS (16.05.2013)

The course should give insight into the basics

of Markov chains with general state space which are necessary for

understanding the theoretical properties of MCMC methods. Students

should become familiar with commonly used MCMC algorithms and after

the course they should be able to apply those algorithms to problems

in Bayesian and spatial statistics.

Course completion requirements -
Last update: RNDr. Michaela Prokešová, Ph.D. (05.10.2022)

The course is finalized by a credit from exercise class and by a final exam.

The credit from exercise class is necessary for taking part in the final exam.

Requirements for receiving the credit from exercise class:

1) active participance in the exercise class and handing in the 5 assigned homework exercises


2) solution of the credit homework assignment (includes theoretical analysis and practical implementation of an MCMC algorithm for a particular problem).

Attempt to receive the credit from exercise class cannot be repeated.

Literature -
Last update: RNDr. Michaela Prokešová, Ph.D. (08.10.2015)

S. Brooks, A. Gelman, G. L. Jones, X. Meng (2011): Handbook of Markov Chain Monte Carlo, Chapman & Hall/CRC, Boca Raton.

D. Gamerman a H. F. Lopes (2006): Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, 2nd ed., Chapman & Hall/CRC, Boca Raton.

W. S. Kendall, F. Liang, L.-S. Wang (Eds.) (2005): Markov Chain Monte Carlo: Innovations and Applications, World Scientific, Singapore.

S. P. Meyn a R. L. Tweedie (2009): Markov Chains and Stochastic Stability, 2nd ed., Cambridge University Press, Cambridge.

C. P. Robert (2001): The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, druhé vydání, Springer, New York.

Teaching methods -
Last update: T_KPMS (16.05.2013)


Requirements to the exam -
Last update: RNDr. Michaela Prokešová, Ph.D. (01.08.2018)

The final exam is oral. All material covered during the course may be part of the exam.

Syllabus -
Last update: RNDr. Michaela Prokešová, Ph.D. (25.09.2020)

1. Examples of simulation methods.

2. Bayesian statistics, hierarchical models.

3. Examples of MCMC algorithms, Gibbs sampler, Metropolis-Hastings


4. Theory of Markov chains with general state space.

5. Ergodicity of MCMC algorithms.

6. Practical aspects and estimation of limit variance.

7. Metropolis-Hastings-Green algorithm.

8. Point processes, birth-death Metropolis-Hastings algorithm.

9. Further applications.

Entry requirements -
Last update: RNDr. Michaela Prokešová, Ph.D. (30.05.2018)

Conditional probability and conditional mean value, discrete time Markov chains with discrete state-space including stationary and limit distributions and ergodicity theorem for these Markov chains.

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