On random- and systematic-scan samplers

Christophe Andrieu

doi:10.1093/biomet/asw019

On random- and systematic-scan samplers

Christophe Andrieu

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Abstract

We introduce a simple time-homogeneous Markov embedding of a class of time-inhomogeneous Markov chains widely used in the context of Monte Carlo sampling algorithms, such as systematic-scan Metropolis-within-Gibbs samplers. This allows us to establish that systematic-scan samplers involving two factors are always better than their random-scan counterparts, when asymptotic variance is the criterion of interest. We also show that this embedding sheds some light on the result of Maire et al. (2014) and discuss the scenario involving more than two factors.

Original language	English
Pages (from-to)	719-726
Number of pages	8
Journal	Biometrika
Volume	103
Issue number	3
Early online date	24 Aug 2016
DOIs	https://doi.org/10.1093/biomet/asw019
Publication status	Published - Sept 2016

Keywords

Deterministic-scan sampler
Markov chain Monte Carlo
Metropolis-within-Gibbs algorithm
Peskun order
Random-scan sampler

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10.1093/biomet/asw019

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Oxford University Press at http://biomet.oxfordjournals.org/content/103/3.toc.
Accepted author manuscript, 267 KB
Supplementary information PDF
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Oxford University Press at http://biomet.oxfordjournals.org/content/103/3.toc.
Accepted author manuscript, 166 KB

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AB - We introduce a simple time-homogeneous Markov embedding of a class of time-inhomogeneous Markov chains widely used in the context of Monte Carlo sampling algorithms, such as systematic-scan Metropolis-within-Gibbs samplers. This allows us to establish that systematic-scan samplers involving two factors are always better than their random-scan counterparts, when asymptotic variance is the criterion of interest. We also show that this embedding sheds some light on the result of Maire et al. (2014) and discuss the scenario involving more than two factors.

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KW - Markov chain Monte Carlo

KW - Metropolis-within-Gibbs algorithm

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JO - Biometrika

JF - Biometrika

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ER -

On random- and systematic-scan samplers

Abstract

Keywords

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Bayesian Inference for Big Data with Stochastic Gradient Markov Chain Monte Carlo

Intractable Likelihood: New Challenges from Modern Applications (ILike)

Professor Christophe Andrieu

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On random- and systematic-scan samplers

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Keywords

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Bayesian Inference for Big Data with Stochastic Gradient Markov Chain Monte Carlo

Intractable Likelihood: New Challenges from Modern Applications (ILike)

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Professor Christophe Andrieu

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