Course detail
Stochastic Modelling
FSI-S2M Acad. year: 2026/2027 Winter semester
The course focuses on Markov Chain Monte Carlo (MCMC) algorithms.
The first part deals with the fundamentals of the theory of Markov chains with continuous (real-valued) state spaces and the existence of their stationary distributions.
Next, it describes the derivation of algorithms that implement these chains and analyzes their convergence.
The final part presents examples of MCMC applications in data analysis and machine learning.
Language of instruction
Czech
Number of ECTS credits
3
Supervisor
Department
Entry knowledge
Probability theory and mathematical statistics, mathematical and functional analysis.
Rules for evaluation and completion of the course
Preparation of a semester project and an oral examination.
Aims
The course objective is to make students familiar with selected parts from probability theory and mathematical statistics, which extend students` knowledge acquired in previous courses. In addition other methods for modelling technical processes on PC are introduced.
Students acquire needed knowledge from important parts of the probability theory and mathematical statistics, which will enable them to use PC model and optimize responsible characteristics and properties of technical systems and processes.
The study programmes with the given course
Programme N-MAI-P: Mathematical Engineering, Master's, elective
Type of course unit
Exercise
26 hours, compulsory
Syllabus
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