Some Tools for Sampling Complex Probability Distributions
Department of Mathematics
University of Chicago
This talk will survey my efforts with coworkers to develop and analyze Monte Carlo sampling algorithms for complex (usually high dimensional) probability distributions. The algorithms can be used to estimate both equilibrium and dynamic properties of a system. For example in the context of computational statistical mechanics we can use these tools to compute free energy differences or reaction rates. I'll also show applications to filtering and prediction for an ocean current as well as an exoplanet parameter estimation problem.
These sampling problems are typically difficult because they are badly scaled and/or they have energetic or entropic barriers separating metastable regions. They cannot be solved accurately by standard sampling methods.