Stochastic Modelling (FSI-S2M)

Academic year 2026/2027
Supervisor: doc. Mgr. Zuzana Hübnerová, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:

Introduction of students to the basics of the theory of Markov chains with a continuous state variable and their use for sample generation. Students will gain an overview of the application of this theory in Bayesian estimation and in typical examples of engineering practice.  
Learning outcomes and competences:
 
Prerequisites:

Probability theory and mathematical statistics, mathematical and functional analysis.
Course contents:

Introduction of students to the basics of the theory of Markov chains with a continuous state variable and their use for sample generation. Students will gain an overview of the application of this theory in Bayesian estimation and in typical examples of engineering practice.  
Teaching methods and criteria:
 
Assesment methods and criteria linked to learning outcomes:

Preparation of a semester project and an oral examination.
Controlled participation in lessons:
 
Type of course unit:
    Exercise  13 × 2 hrs. compulsory                  
Course curriculum:
    Exercise

Probability measure, Bayesian estimations, motivation for using MCMC
Markov chains with discrete state space (ergodic and reversible chains)
Markov chains with continuous state space
Stationary distribution of a Markov chain
Metropolis and Metropolis-Hastings algorithms
Effect of proposal density, rejection criterion, autoregressive function, Gibbs algorithm
Evaluation of MCMC algorithm results
Hamilton’s equations, Hamiltonian Monte Carlo, parameter selection in HMC, No-U-Turn algorithm
Bayesian regression, Bayesian neural networks
Natural language processing (Latent Dirichlet Allocation)
Bayesian inverse problem (parameter estimation in differential equations)
Graph tasks, combinatorial problems, traveling salesman problem
Literature - fundamental:
1.

Charles J. Geyer, Markov Chain Monte Carlo: Lecture notes, University of Minnesota, 2005
2.

Charles J. Geyer, Bayesian Inference via Markov Chain Monte Carlo (MCMC), University of Minnesota, 2025
3.

Hanada, M., Matsuura, S. MCMC from Scratch: A Practical Introduction to Markov Chain Monte Carlo. Springer Nature, 2022.
Literature - recommended:
4.

Brooks, S., Gelman, A., Jones, G., and Meng, X.-L. Handbook of Markov Chain Monte Carlo. Chapman and Hall/CRC, 2011.
5. Gamerman, D., Lopes, H. F, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman & Hall/CRC Texts in Statistical Science, CRC Press, 2006.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
N-MAI-P full-time study --- no specialisation -- GCr 3 Elective 2 1 W