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

摘要

The “weighted ensemble” method, introduced by Huber and Kim Biophys. J. 70, 97 (1996), is oneof a handful of rigorous approaches to path sampling of rare events. Expanding earlier discussions,we show that the technique is statistically exact for a wide class of Markovian and non-Markoviandynamics. The derivation is based on standard path-integral (path probability) ideas, but recasts theweighted-ensemble approach as simple “resampling” in path space. Similar reasoning indicates thatarbitrary nonstatic binning procedures, which merely guide the resampling process, are also valid.Numerical examples confirm the claims, including the use of bins which can adaptively find thetarget state in a simple model.