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Statistics and Computing

, Volume 18, Issue 4, pp 435–446 | Cite as

Differential Evolution Markov Chain with snooker updater and fewer chains

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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 t3 distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the model.

Keywords

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

© The Author(s) 2008

Authors and Affiliations

  1. 1.BiometrisWageningen University and Research CentreWageningenThe Netherlands
  2. 2.Center for NonLinear Studies (CNLS)Los Alamos National LaboratoryLos AlamosUSA

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