Imperial College London
Alternate

DrAndrewDuncan

Faculty of Natural Sciences, Department of Mathematics

Senior Lecturer in Statistics and Data-Centric Engineering
 
 
 
//

Contact

 

a.duncan

 
 
//

Location

 

6M14Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Bierkens:2017:10.1017/apr.2017.22,
author = {Bierkens, J and Duncan, A},
doi = {10.1017/apr.2017.22},
journal = {Advances in Applied Probability},
pages = {791--825},
title = {Limit theorems for the zig-zag process},
url = {http://dx.doi.org/10.1017/apr.2017.22},
volume = {49},
year = {2017}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Bierkens,J
AU  - Duncan,A
DO  - 10.1017/apr.2017.22
EP  - 825
PY  - 2017///
SN  - 0001-8678
SP  - 791
TI  - Limit theorems for the zig-zag process
T2  - Advances in Applied Probability
UR  - http://dx.doi.org/10.1017/apr.2017.22
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000416417500006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/84899
VL  - 49
ER  -
Download