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 one of 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-Markovian dynamics. The derivation is based on standard path-integral (path probability) ideas, but recasts the weighted-ensemble approach as simple “resampling” in path space. Similar reasoning indicates that arbitrary 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 the target state in a simple model. © 2010 American Institute of Physics Article Outline INTRODUCTION THEORY The WE procedure Resampling Statistical description of discretized stochastic trajectories Resampling a distribution of trajectories WE as resampling Resampling in WE simulation can be achieved with arbitrary dynamically changing bins NUMERICAL RESULTS Colored noise Myopic self-avoiding walk WE method with random number of bins WE method with adaptive Voronoi bins DISCUSSION How resampling can improve efficiency in WE simulation Improved efficiency is not guaranteed Connection to other methods CONCLUSIONS