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    Accepted author manuscript, 590 KB, PDF document


Markov chain Monte Carlo (MCMC) 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 Bierkens and Roberts (2016), which proved to provide a highly scalable sampling scheme for sampling in the big data regime; see Bierkens et al. (2016). 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 holds and characterise 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. Based on our results we compare the performance of the zig-zag sampler to existing Monte Carlo methods, both analytically and through simulations.

Original languageEnglish
Pages (from-to)791-825
Number of pages35
JournalAdvances in Applied Probability
Issue number3
Publication statusPublished - 2017

    Research areas

  • central limit theorem, continuous-time Markov process, functional central limit theorem, MCMC, nonreversible Markov process, piecewise deterministic Markov process

ID: 31195596