Convergence of adaptive direction sampling
Journal of Multivariate Analysis
Journal of Global Optimization
Markov Chain Monte Carlo Sampling using Direct Search Optimization
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Statistics and Computing
Editorial: Special issue on adaptive Monte Carlo methods
Statistics and Computing
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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.