Optimizing the asymptotic convergence rate of the Diaconis-Holmes-Neal sampler

Kranthi K. Gade; Michael L. Overton

doi:10.1016/j.aam.2006.05.003

Optimizing the asymptotic convergence rate of the Diaconis-Holmes-Neal sampler

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

Abstract

We consider the problem of optimizing the asymptotic convergence rate of a parameter-dependent nonreversible Markov chain. We begin with a single-parameter case studied by Diaconis, Holmes and Neal and then introduce multiple parameters. We use nonsmooth analysis to investigate whether the presence of multiple parameters allows a faster asymptotic convergence rate, and argue that for a specific parameterization, it does not, at least locally.

Original language	English (US)
Pages (from-to)	382-403
Number of pages	22
Journal	Advances in Applied Mathematics
Volume	38
Issue number	3
DOIs	https://doi.org/10.1016/j.aam.2006.05.003
State	Published - Mar 2007

Keywords

Diaconis-Holmes-Neal sampler
Markov chain optimization
Nonreversible Markov chains
Spectral functions
Variational analysis

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2006.05.003

Cite this

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title = "Optimizing the asymptotic convergence rate of the Diaconis-Holmes-Neal sampler",

abstract = "We consider the problem of optimizing the asymptotic convergence rate of a parameter-dependent nonreversible Markov chain. We begin with a single-parameter case studied by Diaconis, Holmes and Neal and then introduce multiple parameters. We use nonsmooth analysis to investigate whether the presence of multiple parameters allows a faster asymptotic convergence rate, and argue that for a specific parameterization, it does not, at least locally.",

keywords = "Diaconis-Holmes-Neal sampler, Markov chain optimization, Nonreversible Markov chains, Spectral functions, Variational analysis",

author = "Gade, {Kranthi K.} and Overton, {Michael L.}",

note = "Funding Information: We thank Persi Diaconis for introducing us to the work described in [11] and commenting on a first draft of this paper. We also wish to thank an anonymous referee whose comments have improved the quality of the paper. We are also grateful to Adrian Lewis for his interest in this work and for many helpful conversations. Both authors were supported in part by National Science Foundation grant DMS-0412049.",

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AU - Gade, Kranthi K.

AU - Overton, Michael L.

N1 - Funding Information: We thank Persi Diaconis for introducing us to the work described in [11] and commenting on a first draft of this paper. We also wish to thank an anonymous referee whose comments have improved the quality of the paper. We are also grateful to Adrian Lewis for his interest in this work and for many helpful conversations. Both authors were supported in part by National Science Foundation grant DMS-0412049.

PY - 2007/3

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N2 - We consider the problem of optimizing the asymptotic convergence rate of a parameter-dependent nonreversible Markov chain. We begin with a single-parameter case studied by Diaconis, Holmes and Neal and then introduce multiple parameters. We use nonsmooth analysis to investigate whether the presence of multiple parameters allows a faster asymptotic convergence rate, and argue that for a specific parameterization, it does not, at least locally.

AB - We consider the problem of optimizing the asymptotic convergence rate of a parameter-dependent nonreversible Markov chain. We begin with a single-parameter case studied by Diaconis, Holmes and Neal and then introduce multiple parameters. We use nonsmooth analysis to investigate whether the presence of multiple parameters allows a faster asymptotic convergence rate, and argue that for a specific parameterization, it does not, at least locally.

KW - Diaconis-Holmes-Neal sampler

KW - Markov chain optimization

KW - Nonreversible Markov chains

KW - Spectral functions

KW - Variational analysis

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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

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ER -

Optimizing the asymptotic convergence rate of the Diaconis-Holmes-Neal sampler

Abstract

Keywords

ASJC Scopus subject areas

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