Coupling control variates for Markov chain Monte Carlo

Jonathan B. Goodman; Kevin K. Lin

doi:10.1016/j.jcp.2009.03.043

Coupling control variates for Markov chain Monte Carlo

Jonathan B. Goodman, Kevin K. Lin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.

Original language	English (US)
Pages (from-to)	7127-7136
Number of pages	10
Journal	Journal of Computational Physics
Volume	228
Issue number	19
DOIs	https://doi.org/10.1016/j.jcp.2009.03.043
State	Published - Oct 20 2009

Keywords

Control variates
Coupling
Markov chain Monte Carlo
Monte Carlo
Nonequilibrium statistical mechanics
Variance reduction

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.jcp.2009.03.043

Cite this

@article{a3d17ff2827443e2a68df8593141677a,

title = "Coupling control variates for Markov chain Monte Carlo",

abstract = "We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.",

keywords = "Control variates, Coupling, Markov chain Monte Carlo, Monte Carlo, Nonequilibrium statistical mechanics, Variance reduction",

author = "Goodman, {Jonathan B.} and Lin, {Kevin K.}",

note = "Funding Information: We thank Peter Glynn for pointing out Refs. [7,19,22] , and the referee for a careful reading and for pointing out references to the operations research literature. JG was supported in part by the Applied Mathematical Sciences Program of the US Department of Energy under Contract DEFG0200ER25053. KL was supported in part by an NSF Mathematical Sciences Postdoctoral Fellowship. ",

year = "2009",

month = oct,

day = "20",

doi = "10.1016/j.jcp.2009.03.043",

language = "English (US)",

volume = "228",

pages = "7127--7136",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "19",

}

TY - JOUR

T1 - Coupling control variates for Markov chain Monte Carlo

AU - Goodman, Jonathan B.

AU - Lin, Kevin K.

N1 - Funding Information: We thank Peter Glynn for pointing out Refs. [7,19,22] , and the referee for a careful reading and for pointing out references to the operations research literature. JG was supported in part by the Applied Mathematical Sciences Program of the US Department of Energy under Contract DEFG0200ER25053. KL was supported in part by an NSF Mathematical Sciences Postdoctoral Fellowship.

PY - 2009/10/20

Y1 - 2009/10/20

N2 - We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.

AB - We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.

KW - Control variates

KW - Coupling

KW - Markov chain Monte Carlo

KW - Monte Carlo

KW - Nonequilibrium statistical mechanics

KW - Variance reduction

UR - http://www.scopus.com/inward/record.url?scp=68549136477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68549136477&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2009.03.043

DO - 10.1016/j.jcp.2009.03.043

M3 - Article

AN - SCOPUS:68549136477

SN - 0021-9991

VL - 228

SP - 7127

EP - 7136

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 19

ER -

Coupling control variates for Markov chain Monte Carlo

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this