Pierre Nyquist:Parallel tempering and infinite swapping- Understanding the performance and theoretical underpinnings of one of the computational workhorses of the physical sciences

Parallel tempering, or replica exchange, is one of the most used computational methods in areas such as chemical physics, material science etc. It is an MCMC method that enables the computation of quantities that otherwise elude us, one such example being the so-called heat capacity for complicated molecular structures. In this talk we will review the parallel tempering method as well as its so-called infinite swapping limit, both of which correspond to a collection of interacting particles. Focusing on infinite swapping, we then employ a large deviation analysis and methods from stochastic optimal control to discuss certain qualitative properties of the simulation methods (or, equivalently, the underlying stochastic processes). We will discuss a diagnostic based on temperature assignments, how symmetry properties of the underlying potential landscape may affect convergence properties and how the large deviation rate function identifies this, as well as those parts of the state space where noise due to sampling has the greatest impact on the overall performance. This is based on joint work with Jim Doll and Paul Dupuis.