Limit theorems for the Zig-Zag process

Duncan, Andrew and Bierkins, Joris (2017) Limit theorems for the Zig-Zag process. Advances in Applied Probability. ISSN 0001-8678 (Accepted)

[img] PDF - Accepted Version
Restricted to SRO admin only

Download (583kB)


Markov chain Monte Carlo methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition kernel is obtained via the Metropolis-Hastings algorithm, there has been recent interest in alternative schemes based on piecewise deterministic Markov processes (PDMPs). One such approach is based on the Zig-Zag process, introduced in [3], which proved to provide a highly scalable sampling scheme for sampling in the big data regime [2]. In this paper we study the performance of the Zig-Zag sampler, focusing on the one-dimensional case.

In particular, we identify conditions under which a Central limit theorem (CLT) holds and characterize the asymptotic variance. Moreover, we study the influence of the switching rate on the diffusivity of the Zig-Zag process by identifying a diffusion limit as the switching rate tends to infinity. Based on our results we compare the performance of the Zig-Zag sampler to existing Monte Carlo methods, both analytically and through simulations.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 15 Jun 2017 11:00
Last Modified: 15 Jun 2017 11:03

View download statistics for this item

📧 Request an update