  The weighted ensemble (WE) method, an enhanced sampling approach based on
periodically replicating and pruning trajectories in a set of parallel
simulations, has grown increasingly popular for computational biochemistry
problems, due in part to improved hardware and the availability of modern
software. Algorithmic and analytical improvements have also played an important
role, and progress has accelerated in recent years. Here, we discuss and
elaborate on the WE method from a mathematical perspective, highlighting recent
results which have begun to yield greater computational efficiency. Notable
among these innovations are variance reduction approaches that optimize
trajectory management for systems of arbitrary dimensionality.
