Ensemble preconditioning for Markov chain Monte Carlo simulation

Benedict Leimkuhler, Charles Matthews, Jonathan Weare

Research output: Contribution to journalArticle

Abstract

We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighbouring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics, thus providing a practical approach to difficult anisotropic sampling problems in high dimensions. Numerical experiments with model problems demonstrate that dramatic potential speedups, compared to various alternative schemes, are attainable.

Original languageEnglish (US)
Pages (from-to)277-290
Number of pages14
JournalStatistics and Computing
Volume28
Issue number2
DOIs
StatePublished - Mar 1 2018

Fingerprint

Markov Chain Monte Carlo Simulation
Preconditioning
Markov processes
Ensemble
Covariance Information
Multiplicative Noise
Markov Chain Monte Carlo Methods
Replica
Higher Dimensions
Monte Carlo methods
Eliminate
Numerical Experiment
Sampling
Path
Alternatives
Demonstrate
Experiments
Monte Carlo simulation
Markov chain Monte Carlo
Model

Keywords

  • BFGS
  • Brownian dynamics
  • Computational statistics
  • Langevin methods
  • Machine learning
  • Markov chain Monte Carlo
  • MCMC
  • Stochastic sampling

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

Cite this

Ensemble preconditioning for Markov chain Monte Carlo simulation. / Leimkuhler, Benedict; Matthews, Charles; Weare, Jonathan.

In: Statistics and Computing, Vol. 28, No. 2, 01.03.2018, p. 277-290.

Research output: Contribution to journalArticle

Leimkuhler, Benedict ; Matthews, Charles ; Weare, Jonathan. / Ensemble preconditioning for Markov chain Monte Carlo simulation. In: Statistics and Computing. 2018 ; Vol. 28, No. 2. pp. 277-290.
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