Waste-Recycling Monte Carlo

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Abstract

The Metropolis (Markov Chain) Monte Carlo method is simple and powerful. Since 1953, many extensions of the original Markov Chain Monte Carlo method have been proposed, but they are all based on the original Metropolis prescription that only states belonging to the Markov Chain should be sampled. In particular, if trial moves to a potential target state are rejected, that state is not included in the sampling. I will argue that the efficiency of effectively all Markov Chain MC schemes can be improved by including the rejected states in the sampling procedure. Such an approach requires only a trivial (and cheap) extension of existing programs. I will demonstrate that the approach leads to improved estimates of the energy of a system and that it leads to better estimates of free-energy landscapes.