V5F3 Reversible Markov Processes and MCMC methods
Reversible Markov Processes and MCMC methods, Summer semester 2020
Tuesdays 8.15-10.00, Fridays 10.15-12.00, Online/Room 1.008, Endenicher Allee 60
Please register via eCampus if you would like to attend the course:
The course consists of online lectures via Zoom.
Exam: oral, Wednesday 12.8., Tuesday 18.8., Monday 28.9.
Topics to be covered:
- Markov processes with a given invariant measure: Reversible diffusions and Dirichlet forms, general diffusions with a given invariant measure, Langevin dynamics, time discretization, Metropolis-Hastings algorithms (RWM, MALA, HMC), measure preserving stochastic processes on infinite dimensional state spaces.
- Functional inequalities and convergence to equilibrium: Spectral gap, Poincaré and Logarithmic Sobolev inequalities, Isoperimetric inequalities, Concentration of measure, Central Limit Theorem and Large Deviations for Markov Processes in continuous time.
- Long-time asymptotics and error bounds for Markov Chain Monte Carlo methods: Applications of functional inequalities, couplings of diffusion processes and application to MCMC.
The course is a continuation of the Markov processes course in winter semester, but it should also be accessible for students with a different background.
Lecture Notes: My lecture notes on Markov Processes are available here. We will start with Section 7; further sections will be added during the course
Further literature:
- Lecture notes on functional inequalities by Joe Neeman.
- Royer: An initiation to logarithmic Sobolev inequalities
- Stroock: An introduction to Markov processes
- Bakry/Gentil/Ledoux: Analysis and geometry of Markov diffusion operators
- Malrieu: Processus de Markov et inégalités fonctionelles (Lecture notes)
July 2020 Andreas Eberle eberle@uni-bonn.de