Unbiased trajectory-based estimation of stationary distributions and splitting probabilities

Despite many years of progress, procedures to harvest both kinetic and mechanistic observables from a set of unbiased molecular dynamics trajectories are still being optimized. Here we present an approach that exploits stationarity properties to yield both equilibrium and non-equilibrium observables. The method makes no Markov assumption, produces unbiased estimates of observables, and appears to fully harvest information residing in continuous trajectories. The approach can be realized through an iterative procedure, which we demonstrate to be equivalent to an efficient matrix formulation. Most notably, the method is able to resolve committor (splitting probability) values even for rarely visited states in the transition region between designated macrostates. We demonstrate the approach in toy and atomistic protein systems.