Differential Evolution Markov Chain with snooker updater and fewer chains

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.