Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling

J.A. Vrugt, C.J.F. ter Braak, C.G.H. Diks, B.A. Robinson, J.M. Hyman, D. Higdon

Research output: Contribution to journalArticleAcademicpeer-review

670 Citations (Scopus)

Abstract

Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well-constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled Differential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, high-dimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems
Original languageEnglish
Pages (from-to)273-290
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
Volume10
Issue number3
DOIs
Publication statusPublished - 2009

Keywords

  • metropolis algorithm
  • bayesian-inference
  • optimization
  • regeneration
  • uncertainty
  • adaptation
  • migration
  • samplers
  • proposal
  • models

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