Past Event: Oden Institute Seminar

The parallel replica method for Markov Chains

David Aristoff, Department of Mathematics, Colorado State University

Abstract

Markov chains have widespread applications in computational math, chemistry, physics and statistics. For instance, in Markov chain Monte Carlo, Markov chains are used to estimate deterministic quantities for which closed-form expressions are unknown. Another example is in computational chemistry, where Markov chains are used to model molecular dynamics. Of course, it is essential that the Markov chains can be simulated efficiently. We present a very general algorithm for improving the real-time efficiency of Markov chain simulations. In many cases of practical interest, the chains tend to get "stuck" in certain subsets of configuration space. Our algorithm uses many replicas of the chain, simulated in parallel, to help it get "unstuck". The algorithm can be seen as a generalization of A.F. Voter's parallel replica method for simulating Langevin dynamics.