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Lecturer(s)
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Ježek Vladimír, doc. Ing. Ph.D.
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Course content
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1. Definition and elementary properties of Markov chains with general state space. Classification. Examples. 2. Geometric ergodicity. 3. Gibbs sampler. 4. Metropolis-Hastings algorithm. 5. Applications in statistical physics. 6. Applications in economics and finance. 7. Perfect simulations.
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, Students' portfolio, Task-based study method, Individual study, Students' self-study
- Contact hours
- 39 hours per semester
- Individual project (40)
- 40 hours per semester
- Preparation for an examination (30-60)
- 40 hours per semester
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| prerequisite |
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| Knowledge |
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| Students should have a basic knowledge of probability theory (KMA/PSA) and of fundamentals of random processes (KMA/ZNP). |
| learning outcomes |
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| Students taking this course will be able to grasp the Markov Chain Monte Carlo (MCMC) method and namely: - recognize and classify Markov chain with general state space and name their basic properties, - apply Gibbs sampler, Metropolis-Hastings algorithm and perfect simulations to practical problems in statistical physics, economics and finance, - provide logical and coherent proofs of theoretic results, - solve problems via abstract methods, - apply correctly formal and rigorous competency in mathematical presentation, both in written and verbal form. |
| teaching methods |
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| Lecture supplemented with a discussion |
| Interactive lecture |
| Task-based study method |
| Self-study of literature |
| Individual study |
| Students' portfolio |
| assessment methods |
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| Oral exam |
| Written exam |
| Seminar work |
| Individual presentation at a seminar |
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Recommended literature
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David P. Landau, Kurt Binder. A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press, 2000. ISBN 0521653665.
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W. S. Kendall, F. Liang, J. S. Wang. Markov Chain Monte Carlo: Innovations and Applications. World Scientific Publishing Co Pte Ltd, 2005. ISBN 978-9812564276.
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