Markov Chains [not a book review]

As Randal Douc and Éric Moulines are both very close friends and two authors of this book on Markov chains,  I cannot engage into a regular book review! Judging from the table of contents, the coverage is not too dissimilar to the now classic Markov chain Stochastic Stability book by Sean Meyn and the late Richard Tweedie (1994), called the Bible of Markov chains by Peter Glynn, with more emphasis on convergence matters and a more mathematical perspective. The 757 pages book also includes a massive appendix on maths and probability background. As indicated in the preface, “the reason [the authors] thought it would be useful to write a new book is to survey some of the developments made during the 25 years that have elapsed since the publication of Meyn and Tweedie (1993b).” Connecting with the theoretical developments brought by MCMC methods. Like subgeometric rates of convergence to stationarity, sample paths, limit theorems, and concentration inequalities. The book also reflects on the numerous contributions of the authors to the field. Hence a perfect candidate for teaching Markov chains to mathematically well-prepared. graduate audiences. Congrats to the authors!

Sean Meyn in Paris

My friend Sean Meyn (from the University of Florida, Gainesville) will give a talk in Paris next week (and I will be away in Coventry at the time…). Here are the details:

Mardi 26 novembre 2013 à 14h00
Salle de Conseil, 4ème étage (LINCS) 23 AVENUE D’ITALIE 75013 PARIS

Titre de l’exposé : Feature Selection for Neuro-Dynamic Programming

Neuro-Dynamic Programming encompasses techniques from both reinforcement learning and approximate dynamic programming. Feature selection refers to the choice of basis that defines the function class that is required in the application of these techniques. This talk reviews two popular approaches to neuro-dynamic programming, TD-learning and Q-learning. The main goal of this work is to demonstrate how insight from idealized models can be used as a guide for feature selection for these algorithms. Several approaches are surveyed, including fluid and diffusion models, and the application of idealized models arising from mean-field game approximations. The theory is illustrated with several examples.