Markov chains and markov models
Feliks Nüske
Zusätzl. Angaben / Voraussetzungen
Master students of Mathematics and Physics
Kommentar
Markov chains are widely used to model stochastic behaviour across the sciences. In this course, we will focus on their application to model dynamical phenomena in the natural and engineering sciences. In the first half of the course, we will study the stationary and spectral properties of discrete Markov chains and how they can be used to analyse the long-time behaviour of the chain. In the second half, we will learn how to construct continuous Markov chains to sample complex probability distributions, and how to construct suitable discrete models for their approximation.
Discrete Markov Chains
- introduction and basic properties
- stationary vectors and return times
- spectral decomposition, reversible chains
- Perron cluster analysis
- committors and transition path theory
Modeling with Markov Chains
- Markov chains on continuous space
- sampling and Markov chain Monte Carlo
- Markov state models (MSMs)
- MSM estimation based on maximum likelihood
- error analysis
13 Termine
Regelmäßige Termine der Lehrveranstaltung