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Speed Up Zig-Zag

Lookup NU author(s): Dr Giorgos VasdekisORCiD

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

Abstract

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, including 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 providing an efficiency criterion for the one-dimensional process and we support our findings with simulation results.

Publication metadata

Author(s): Vasdekis G, Roberts GO

Publication type: Article

Publication status: Published

Journal: Annals of Applied Probability

Year: 2023

Volume: 33

Issue: 6A

Pages: 4693-4746

Print publication date: 04/12/2023

Online publication date: 04/12/2023

Acceptance date: 05/01/2023

Date deposited: 20/06/2024

ISSN (print): 1050-5164

ISSN (electronic): 2168-8737

Publisher: Institute of Mathematical Statistics

URL: https://doi.org/10.1214/23-AAP1930

DOI: 10.1214/23-AAP1930

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