ACMD Seminar: Stratification for Markov chain Monte Carlo sampling

Jonathan Weare
Department of Statistics, University of Chicago

Tuesday, June 27, 2017, 15:30 - 16:30
Building 101, Lecture Room F
Gaithersburg

Tuesday, June 27, 2017, 13:30 - 14:30
Room 1-4058
Boulder

Presentation Slides

Host: Michael Mascagni

Abstract: I will discuss an ensemble sampling scheme based on a decomposition of the target average of interest into subproblems that are each individually easier to solve and can be solved in parallel. The most basic version of the scheme computes averages with respect to a given density and is a generalization of the Umbrella Sampling method for the calculation of free energies. We have developed a careful understanding of the accuracy of the scheme that is sufficiently detailed to explain the success of umbrella sampling in practice and to suggest improvements including adaptivity. For equilibrium versions of the scheme we have developed error bounds that reveal that the existing understanding of umbrella sampling is incomplete and leads to a number of erroneous conclusions about the scheme. Our bounds are motivated by new perturbation bounds for Markov Chains that we recently established and that are substantially more detailed than existing perturbation bounds for Markov chains. They demonstrate, for example, that equilibrium umbrella sampling is robust in the sense that in limits in which the straightforward approach to sampling from a density becomes exponentially expensive, the cost to achieve a fixed accuracy with umbrella sampling can increase only polynomially.

Bio: Jonathan Weare is an assistant professor in the Department of Statistics at The University of Chicago and part of the Committee on Computational and Applied Mathematics there. He is also an assistant professor in the James Franck Institute. Before joining the Statistics Department, Jonathan was an assistant professor in the Department of Mathematics at the University of Chicago and, before moving to Chicago, he was a Courant Instructor of mathematics at NYU and a PhD student in mathematics at the University of California at Berkeley. In his research, Jonathan makes use of tools from probability theory, the theory of partial differential equations, and numerical analysis, to analyze interesting physical phenomena and to design, analyze, and apply new computational techniques to study challenging problems arising in the physical sciences and engineering. His current application areas of interest include the dynamics of crystal surfaces, molecular simulation problems in chemistry and bio-chemistry, power systems, extreme climate and weather events, and geophysical data assimilation.