Limit theorems for the zig-zag process

Bierkens, Joris and Duncan, Andrew (2017) Limit theorems for the zig-zag process. Advances in Applied Probability, 49 (03). pp. 791-825. ISSN 0001-8678

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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: Catrina Hey
Date Deposited: 14 Nov 2017 13:29
Last Modified: 16 Nov 2017 12:56

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