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Markov Chain Monte Carlo Methods - NSTP139

Title:	Metody MCMC (Markov Chain Monte Carlo)
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	RNDr. Michaela Prokešová, Ph.D.
Class:	DS, pravděpodobnost a matematická statistika
Classification:	Mathematics > Probability and Statistics
Interchangeability :	NMTP539

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Annotation -

Last update: T_KPMS (16.05.2012)

Markov chains with general state space, geometric ergodicity. Gibbs sampler, Metropolis-Hastings algorithm, properties and applications. Recommended qualifications: knowledge in the range of the courses Probability theory 1, Stochastic processes 1.

Aim of the course -

Last update: T_KPMS (19.05.2008)

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.

Literature -

Last update: T_KPMS (19.05.2008)

D. Gamerman a H. F. Lopes (2006): Markov Chain Monte Carlo: Stochastic

Simulation for Bayesian Inference, druhé vydání, Chapman & Hall/CRC, Boca

Raton.

W. Gilks, S. Richardson a D. Spiegelhalter (1996): Markov Chain Monte Carlo

in Practice, Chapman & Hall, London.

S. P. Meyn a R. L. Tweedie (1993): Markov Chains and Stochastic Stability,

Springer-Verlag, New York.

C. P. Robert (2001): The Bayesian Choice: From Decision-Theoretic

Foundations to Computational Implementation, druhé vydání, Springer, New

York.

Teaching methods -

Last update: G_M (27.05.2008)

Lecture+exercises.

Syllabus -

Last update: T_KPMS (19.05.2008)

1. Examples of simulation methods.

2. Bayesian statistics, hierarchial models.

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

algorithm.

4. Markov chains with general state space.

5. Ergodicity of MCMC algorithms.

6. Simulated annealing, perfect simulation.

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

8. Further applications.