2019/05/31 by Saifuddin Syed, Alexandre Bouchard-Côté, George Deligiannidis +1 · 1 citation
Mathematics · #stat.CO #msc:65C05
paper · pdf · doi:10.1111/rssb.12464
74 pages, 30 figures. The method is implemented in an open source probabilistic programming available at https://github.com/UBC-Stat-ML/blangSDK
arxiv created 2021/07/26 · arxiv updated 2021/07/28
Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of N interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state-space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and performance of reversible versus non-reversible PT schemes. We show theoretically and empirically that a class of non-reversible PT methods dominates its reversible counterparts and identify distinct scaling limits for the non-reversible and reversible schemes, the former being a piecewise-deterministic Markov process and the latter a diffusion. These results are exploited to identify the optimal annealing schedule for non-reversible PT and to develop an iterative scheme approximating this schedule. We provide a wide range of numerical examples supporting our theoretical and methodological contributions. The proposed methodology is applicable to sample from a distribution π with a density L with respect to a reference distribution π0 and compute the normalizing constant. A typical use case is when π0 is a prior distribution, L a likelihood function and π the corresponding posterior.