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Limit theorems for the zig-zag process
journal contribution
posted on 2023-06-09, 08:49 authored by Joris Bierkens, Andrew DuncanMarkov 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 ProbabilityISSN
0001-8678Publisher
Applied Probability TrustExternal DOI
Issue
03Volume
49Page range
791-825Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-11-14First Open Access (FOA) Date
2017-11-14First Compliant Deposit (FCD) Date
2017-11-14Usage metrics
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