Differential Evolution Markov Chain with snooker updater and fewer chains |
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Authors: | Cajo J F ter Braak Jasper A Vrugt |
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Institution: | (1) Biometris, Wageningen University and Research Centre, Box 100, 6700 AC Wageningen, The Netherlands;(2) Center for NonLinear Studies (CNLS), Los Alamos National Laboratory, Los Alamos, NM 87545, USA |
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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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Keywords: | Evolutionary Monte Carlo Metropolis algorithm Adaptive Markov chain Monte Carlo Theophylline kinetics Adaptive direction sampling Parallel computing Differential evolution |
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