PhD Student, University of British Columbia

Talk Title

Non-Reversible Parallel Tempering: Geometric Ergodicity and MCMC Diagnostics

Abstract

Parallel tempering (PT) is an effective algorithm for sampling from target distributions with complex geometry, such as those arising from posterior distributions in weakly identifiable and/or high-dimensional Bayesian models. Recent developments in the literature have shown that a particular non-reversible version of PT is well-suited for handling such sampling problems. Under an assumption of strongly efficient local exploration kernels in each PT chain—which do not have to be reducible but rather only efficient in their local region—we establish that PT is uniformly geometrically ergodic. Further, the bounds on the rates that we obtain are explicitly related to a divergence referred to as the global communication barrier, which can be easily estimated. We also show that non-reversible parallel tempering with a deterministic communication scheme dominates its reversible counterpart by relating the rates of ergodicity to the hitting times of a persistent and regular random walk, respectively. Additional results are presented that connect geometric ergodicity to useful MCMC diagnostics for practitioners.

Bio

Nikola is a Vanier Scholar pursuing a PhD in Statistics at the University of British Columbia with research interests in scalable Bayesian inference. He is supervised by Dr. Alexandre Bouchard-Côté and Dr. Trevor Campbell.