14ème Journée EDP/Probas

Algorithmes de Metropolis Hastings : des probabilités à l’analyse des équations aux dérivées partielles.

vendredi 7 février 2014

La journée est composée de deux minicours :

10h - 12h : Persi Diaconis (Stanford)

Title : The Metropolis Algorithm : an expository account.

Abstract : The Metropolis/Hasting algorithms and their many variations (hybred Monte Carlo, Metropolis on Gibbs, higher order variants) are a mainstay of scientific computing. I will try to make sense of the variants, explain the underlying geometry (Metropolis gives the closest reversible Markov operator to a given proposal chain) and point to the following facts : we are a million miles away from having useful things to say to practitioners. If you take ANY real application of these algorithms you have an interesting open math problem.

14h15 - 16h15 : Gilles Lebeau (Nice)

Title : Spectral problems in the Metropolis Algorithm.

Abstract : The analysis of the rate of convergence of a Metropolis algorithm involves the study of the spectrum of the associated Markov operator. I will describe the spectral properties of this operator for variants of the historical Metropolis chain applied to hard spheres systems. I will first explain how these spectral properties are related to classical estimates in partial differential equations such as Weyl estimates, Sobolev inequalities, Fourier analysis... Then, I will try to describe some of the numerous new challenges and unsolved problems.

La journée aura lieu dans l’amphithéatre Hermite de l’Institut Henri Poincaré, 11 rue Pierre et Marie Curie, Paris 5éme (accès)