Course detail
Stochastic Modelling
FSI-S2M Acad. year: 2026/2027 Winter semester
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.
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
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.
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