SPEED UP ZIG-ZAG

• 成果类型: Article
• 署名作者: Vasdekis, G.; Roberts, G. O.
• 署名单位: University of London; University College London; University of Warwick
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1930
• 发表日期: 2023
• 页码: 4693-4746
• 关键词: deterministic markov-processes; long-time behavior; geometric ergodicity; monte-carlo; STABILITY; limit

摘要

The Zig-Zag process is a piecewise deterministic Markov process, efficiently used for simulation in an MCMC setting. As we show in this article, it fails to be exponentially ergodic on heavy tailed target distributions. We introduce an extension of the Zig-Zag process by allowing the process to move with a nonconstant speed function s, depending on the current state of the process. We call this process Speed Up Zig-Zag (SUZZ). We provide conditions that guarantee stability properties for the SUZZ process, includ-ing nonexplosivity, exponential ergodicity in heavy tailed targets and central limit theorem. Interestingly, we find that using speed functions that induce explosive deterministic dynamics may lead to stable algorithms that can even mix faster. We further discuss the choice of an efficient speed function by pro-viding an efficiency criterion for the one-dimensional process and we support our findings with simulation results.