Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Asymptotic variance for random walk metropolis chains in high dimensions : logarithmic growth via the Poisson equation

Tools
- Tools
+ Tools

Mijatović, Aleksandar and Vogrinc, Jure (2019) Asymptotic variance for random walk metropolis chains in high dimensions : logarithmic growth via the Poisson equation. Advances in Applied Probability, 51 (4). pp. 994-1026. doi:10.1017/apr.2019.40

[img]
Preview
PDF
WRAP-asymptotic-variance-random-walk-metropolis-chains-high-dimensions-Vogrinc-2019.pdf - Accepted Version - Requires a PDF viewer.

Download (892Kb) | Preview
Official URL: https://doi.org/10.1017/apr.2019.40

Request Changes to record.

Abstract

There are two ways of speeding up Markov chain Monte Carlo algorithms: (a) construct more complex samplers that use gradient and higher-order information about the target and (b) design a control variate to reduce the asymptotic variance. While the efficiency of (a) as a function of dimension has been studied extensively, this paper provides the first results linking the efficiency of (b) with dimension. Specifically, we construct a control variate for a d-dimensional random walk Metropolis chain with an independent, identically distributed target using the solution of the Poisson equation for the scaling limit in [30]. We prove that the asymptotic variance of the corresponding estimator is bounded above by a multiple of over the spectral gap of the chain. The proof hinges on large deviations theory, optimal Young’s inequality and Berry–Esseen-type bounds. Extensions of the result to non-product targets are discussed.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Random walks (Mathematics), Asymptotic expansions
Journal or Publication Title: Advances in Applied Probability
Publisher: Applied Probability Trust
ISSN: 0001-8678
Official Date: December 2019
Dates:
DateEvent
December 2019Published
17 June 2019Accepted
Volume: 51
Number: 4
Page Range: pp. 994-1026
DOI: 10.1017/apr.2019.40
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: Accepted for publication by the Applied Probability Trust (http://www.appliedprobability.org) in Advances in Applied Probability, 51 (4).
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: © Applied Probability Trust 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/P003818/1 [EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
UNSPECIFIEDLloyd’s Register FoundationUNSPECIFIED
EP/P002625/[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/R022100/[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
Related URLs:
  • Publisher
  • Publisher

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us