Improving MCMC samplers with spectral theory and optimal transport

02.03.2018, 10:15-11:15  –  Haus 28, Raum 0.104

Nikolas Nüsken (Imperial College London)

Markov Chain Monte Carlo methods are popular tools in Bayesian statistics and molecular dynamics to draw samples from a given probability distribution, using appropriate ergodic stochastic dynamics. This talk will address two approaches to modify well-known sampling strategies in order to improve their convergence properties, quantified in terms of central limit theorems and spectral gap estimates. The first part is concerned with nonreversible perturbations of underdamped Langevin dynamics, where the analysis focuses on spectral analysis of the associated infinitesimal generator. The second part will address coupling approaches for multi-particle samplers and their relation to optimal transportation problems. 

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