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Differential Evolution Markov Chain with snooker updater and fewer chains

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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Correspondence to Cajo J. F. ter Braak.

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

Keywords

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