  The dynamics of molecules are governed by rare event transitions between
long-lived (metastable) states. To explore these transitions efficiently, many
enhanced sampling protocols have been introduced that involve using simulations
with biases or changed temperatures. Two established statistically optimal
estimators for obtaining unbiased equilibrium properties from such simulations
are the multistate Bennett Acceptance Ratio (MBAR) and the transition-based
reweighting analysis method (TRAM). Both MBAR and TRAM are solved iteratively
and can suffer from long convergence times. Here we introduce stochastic
approximators (SA) for both estimators, resulting in SAMBAR and SATRAM, which
are shown to converge faster than their deterministic counterparts, without
significant accuracy loss. Both methods are demonstrated on different molecular
systems.
