bRiteWeight: Randomized iterative reweighting for biased trajectory data

Determining the stationary distribution from a set of stochastic-process trajectory data, e.g., molecular dynamics, has long been a challenging if under-appreciated problem. We recently proposed a randomized iterative reweighting algorithm, “RiteWeight,” which provided a solution given unbiased trajectory data, i.e., trajectories generated directly from the dynamics of interest (potential surface, temperature, etc.). However, numerous sampling methodologies use biased dynamics, typically generated from a smoothed energy surface. Here, we introduce the bRiteWeight algorithm, which modifies RiteWeight for biased dynamics based on Girsanov (importance sampling) weights for trajectory snippets. We show theoretically and with simple examples that the new algorithm can correct biased dynamics to yield the stationary distribution of the unbiased system. As with RiteWeight, the algorithm is suitable both for equilibrium and nonequilibrium steady states.