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Differential Evolution Markov Chain with snooker updater and fewer chains

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  • Published: 21 October 2008
  • volume 18, pages 435–446 (2008)
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Differential Evolution Markov Chain with snooker updater and fewer chains
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  • Cajo J. F. ter Braak1 &
  • Jasper A. Vrugt2 
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  • 344 Citations

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Abstract

Differential Evolution Markov Chain (DE-MC) is an adaptive MCMC algorithm, in which multiple chains are run in parallel. Standard DE-MC requires at least N=2d chains to be run in parallel, where d is the dimensionality of the posterior. This paper extends DE-MC with a snooker updater and shows by simulation and real examples that DE-MC can work for d up to 50–100 with fewer parallel chains (e.g. N=3) by exploiting information from their past by generating jumps from differences of pairs of past states. This approach extends the practical applicability of DE-MC and is shown to be about 5–26 times more efficient than the optimal Normal random walk Metropolis sampler for the 97.5% point of a variable from a 25–50 dimensional Student t 3 distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the model.

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Authors and Affiliations

  1. Biometris, Wageningen University and Research Centre, Box 100, 6700 AC, Wageningen, The Netherlands

    Cajo J. F. ter Braak

  2. Center for NonLinear Studies (CNLS), Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Jasper A. Vrugt

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  1. Cajo J. F. ter Braak
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  2. Jasper A. Vrugt
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Correspondence to Cajo J. F. ter Braak.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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ter Braak, C.J.F., Vrugt, J.A. Differential Evolution Markov Chain with snooker updater and fewer chains. Stat Comput 18, 435–446 (2008). https://doi.org/10.1007/s11222-008-9104-9

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  • Received: 24 July 2008

  • Accepted: 24 September 2008

  • Published: 21 October 2008

  • Issue Date: December 2008

  • DOI: https://doi.org/10.1007/s11222-008-9104-9

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Keywords

  • Evolutionary Monte Carlo
  • Metropolis algorithm
  • Adaptive Markov chain Monte Carlo
  • Theophylline kinetics
  • Adaptive direction sampling
  • Parallel computing
  • Differential evolution
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