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Limit theorems for the zig-zag process

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journal contribution
posted on 2023-06-09, 08:49 authored by Joris Bierkens, Andrew Duncan
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Advances in Applied Probability

ISSN

0001-8678

Publisher

Applied Probability Trust

Issue

03

Volume

49

Page range

791-825

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-11-14

First Open Access (FOA) Date

2017-11-14

First Compliant Deposit (FCD) Date

2017-11-14

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