PhD open series of lectures

The upcoming PhD open series of lectures will be in MCMC sampling algorithms.

Our speaker will be Samuel Livingstone from University College London. 

Markov chain Monte Carlo sampling algorithms

Abstract: We will cover some mathematical preliminaries and basic sampling and Monte Carlo before discussing Markov chains on general state spaces and Markov chain Monte Carlo. Topics include the Metropolis—Hastings algorithm and in particular the Random Walk Metropolis, some more advanced algorithms based on continuous time stochastic processes such as Langevin diffusions, and some introduction to the study of convergence to equilibrium and asymptotic variance.

Schedule:
2025-04-14, room 5070, 16:15-17:45
2025-04-15, room 5070, 16:15-17:45
2025-04-23, room 5070, 16:15-17:45
2025-04-24, room 5070, 16:15-17:45
2025-04-25, room 5070, 16:15-17:45

A rough syllabus:
1. Mathematical Preliminaries, sampling, Monte Carlo, rejection and importance sampling
2. Markov chains on general state spaces, intro to Markov chain Monte Carlo
3. The Metropolis—Hastings algorithm, random Walk Metropolis, diagnosing good vs bad behaviour, remarks on optimal tuning
4. Some theory (Invariance and convergence to equilibrium, asymptotic variance, remarks on coupling, spectral gaps and Peskun ordering)
5. Advanced algorithms (Langevin diffusions, Momentum & Hamiltonian dynamics, tempering for multi-modal distributions, remarks on
non-reversible algorithms)

The rules for getting ECTS points are described in USOS (course id:1000-1M24WWM).

Please register here: https://forms.gle/sxkFSKRJhEqx<wbr></wbr>Zd4P8