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Reading Seminar Series
Markov Chains and Mixing Times
Venue: Green Room at Eurandom
Name Date Title
Martingales and evolving sets - Chapter 17
The transportation metric and path coupling
I will talk about some topics from chapters 13 and 14, with particular focus on the transportation metric, path coupling, and approximate counting via Markov chains.
Alessandro Di Bucchianico
Simulation via Markov Chain Monte Carlo methods
I will provide an introduction to the use of Markov chains in simulation known as Markov Chain Monte Carlo (MCMC). This technique is widely used in several research areas, including Statistical Physics and Bayesian statistics. I will show the Markov chain setting behind the two main forms (the Gibbs sampler and the Metropolis-Hastings sampler) and put these methods in a wider context of simulation techniques. This presentation is partly based on Chapter 3 of the book and partly based introductory articles on MCMC.
Andrieu, N. De Freitas , A. Doucet, and M.I. Jordan, An Introduction to
MCMC for Machine Learning, Machine Learning 50 (2003), 5-43.
G. Casella and J. Berger, Explaining the
Gibbs Sampler, American Statistician 46 (1992), 167-174.
On this seminar we will explore the connection between
mixing properties of Markov chain and spectral structure
In this session of the reading seminar we will discuss a number of stopping times of random walks on general graphs. We review hitting, random target, commute and cover times. We compute them on some simple graphs and in the process highlight the connections between these times.
In this first meeting we will present some key concepts and tools which will be used during the whole reading seminar, among them the total variation distance and its property, the coupling technique and mixing times. We will then start exploring the deep connections existing between these objects, focusing in particular on the case of Markov chains.
P.O. Box 513, 5600 MB Eindhoven, The Netherlands