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

TL;DR

The paper proves that the weighted ensemble path sampling method is statistically exact for a broad class of stochastic processes, including non-Markovian dynamics, and validates this with numerical examples.

Contribution

It demonstrates the statistical exactness of the weighted ensemble method for diverse stochastic processes and general binning procedures, extending previous understanding.

Findings

The method is statistically exact for Markovian and non-Markovian dynamics.

Arbitrary nonstatic binning procedures are valid for guiding resampling.

Numerical examples confirm the method's effectiveness and adaptability.

Abstract

The "weighted ensemble" method, introduced by Huber and Kim, [G. A. Huber and S. 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.