An Exploration-Agnostic Characterization of the Ergodicity of Parallel Tempering

Explore the ergodicity of parallel tempering in this 48-minute lecture from the Colloque des sciences mathématiques du Québec. Delve into Trevor Campbell's research on non-reversible parallel tempering (NRPT) and its effectiveness in sampling from complex target distributions. Examine the uniform geometric ergodicity of NRPT under an efficient local exploration hypothesis and understand how the global communication barrier (GCB) plays a role in bounding ergodicity rates. Compare NRPT with classical reversible parallel tempering and gain insights into their relative performance. Investigate the properties of GCB and its relationships with total variation distance and Kullback-Leibler divergences. Conclude by reviewing simulations that validate the theoretical analysis presented, based on collaborative work with Nikola Surjanovic, Saifuddin Syed, and Alexandre Bouchard-Côté.