Uniform Ergodicity of Parallel Tempering With Efficient Local Exploration

Understand

Non-reversible parallel tempering (NRPT) is an effective algorithm for sampling from target distributions with complex geometry, such as those arising from posterior distributions of weakly identifiable and high-dimensional Bayesian models.

• In this work we establish the uniform (geometric) ergodicity of NRPT under a model of efficient local exploration.
• The uniform ergodicity log rates are inversely proportional to an easily-estimable divergence, the global communication barrier (GCB), which was recently introduced in the literature.
• We obtain analogous ergodicity results for classical reversible parallel tempering, providing new evidence that NRPT dominates its reversible counterpart.