Particle Markov chain Monte Carlo for efficient numerical simulation

Christophe Andrieu; Arnaud Doucet; Roman Holenstein

doi:10.1007/978-3-642-04107-5-3

Particle Markov chain Monte Carlo for efficient numerical simulation

Christophe Andrieu, Arnaud Doucet, Roman Holenstein

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

20 Citations (Scopus)

Abstract

Markov ChainMonte Carlo (MCMC) and sequentialMonte Carlo (SMC) methods are the two most popular classes of algorithms used to sample from general high-dimensional probability distributions. The theoretical convergence of MCMC algorithms is ensured under weak assumptions, but their practical performance is notoriously unsatisfactory when the proposal distributions used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to systematically design potentially very efficient high-dimensional proposal distributions for MCMC by using SMC techniques. We demonstrate how this novel approach allows us to design effective MCMC algorithms in complex scenarios. This is illustrated by a problem of Bayesian inference for a stochastic kinetic model.

Original language	English
Title of host publication	Monte Carlo and Quasi-Monte Carlo Methods 2008
Publisher	Springer Verlag
Pages	45-60
Number of pages	16
ISBN (Print)	9783642041068
DOIs	https://doi.org/10.1007/978-3-642-04107-5-3
Publication status	Published - 2009
Event	8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2008 - Montreal, QC, Canada Duration: 6 Jul 2008 → 11 Jul 2008

Conference

Conference	8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2008
Country/Territory	Canada
City	Montreal, QC
Period	6/07/08 → 11/07/08

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title = "Particle Markov chain Monte Carlo for efficient numerical simulation",

abstract = "Markov ChainMonte Carlo (MCMC) and sequentialMonte Carlo (SMC) methods are the two most popular classes of algorithms used to sample from general high-dimensional probability distributions. The theoretical convergence of MCMC algorithms is ensured under weak assumptions, but their practical performance is notoriously unsatisfactory when the proposal distributions used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to systematically design potentially very efficient high-dimensional proposal distributions for MCMC by using SMC techniques. We demonstrate how this novel approach allows us to design effective MCMC algorithms in complex scenarios. This is illustrated by a problem of Bayesian inference for a stochastic kinetic model.",

author = "Christophe Andrieu and Arnaud Doucet and Roman Holenstein",

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Andrieu, C, Doucet, A & Holenstein, R 2009, Particle Markov chain Monte Carlo for efficient numerical simulation. in Monte Carlo and Quasi-Monte Carlo Methods 2008. Springer Verlag, pp. 45-60, 8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2008, Montreal, QC, Canada, 6/07/08. https://doi.org/10.1007/978-3-642-04107-5-3

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AU - Doucet, Arnaud

AU - Holenstein, Roman

PY - 2009

Y1 - 2009

N2 - Markov ChainMonte Carlo (MCMC) and sequentialMonte Carlo (SMC) methods are the two most popular classes of algorithms used to sample from general high-dimensional probability distributions. The theoretical convergence of MCMC algorithms is ensured under weak assumptions, but their practical performance is notoriously unsatisfactory when the proposal distributions used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to systematically design potentially very efficient high-dimensional proposal distributions for MCMC by using SMC techniques. We demonstrate how this novel approach allows us to design effective MCMC algorithms in complex scenarios. This is illustrated by a problem of Bayesian inference for a stochastic kinetic model.

AB - Markov ChainMonte Carlo (MCMC) and sequentialMonte Carlo (SMC) methods are the two most popular classes of algorithms used to sample from general high-dimensional probability distributions. The theoretical convergence of MCMC algorithms is ensured under weak assumptions, but their practical performance is notoriously unsatisfactory when the proposal distributions used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to systematically design potentially very efficient high-dimensional proposal distributions for MCMC by using SMC techniques. We demonstrate how this novel approach allows us to design effective MCMC algorithms in complex scenarios. This is illustrated by a problem of Bayesian inference for a stochastic kinetic model.

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SN - 9783642041068

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EP - 60

BT - Monte Carlo and Quasi-Monte Carlo Methods 2008

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T2 - 8th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2008

Y2 - 6 July 2008 through 11 July 2008

ER -

Particle Markov chain Monte Carlo for efficient numerical simulation

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