Mathematical Foundation of Various MCMC Methods

Explore the mathematical foundations of various Markov Chain Monte Carlo (MCMC) methods in this 51-minute lecture by Akira Sakai from Hokkaido University, presented at the Institut des Hautes Etudes Scientifiques (IHES). Delve into combinatorial optimization problems, focusing on approaches using Ising models to tackle challenges like the traveling salesman problem. Examine standard MCMC methods such as Glauber dynamics and the Metropolis algorithm, and their limitations in sampling Gibbs distributions. Discover three alternative MCMC methods, including two based on multi-spin flip rules, potentially offering faster solutions. Gain insights into mathematical and numerical results comparing these methods in different contexts. Learn about the collaborative research conducted as part of a five-year CREST project, involving Bruno Hideki Fukushima-Kimura and other contributors.