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The "weighted ensemble" method, introduced by Huber and Kim, [G. A. Huber andS. Kim, Biophys. J. 70, 97 (1996)], is one of a handful of rigorous approachesto path sampling of rare events. Expanding earlier discussions, we show thatthe technique is statistically exact for a wide class of Markovian andnon-Markovian dynamics. The derivation is based on standard path-integral (pathprobability) ideas, but recasts the weighted-ensemble approach as simple"resampling" in path space. Similar reasoning indicates that arbitrarynonstatic binning procedures, which merely guide the resampling process, arealso valid. Numerical examples confirm the claims, including the use of binswhich can adaptively find the target state in a simple model.

The "weighted ensemble" path sampling method is statistically exact for a broad class of stochastic processes and binning procedures