Automated sampling assessment for molecular simulations using the effective sample size

To quantify the progress in the development of algorithms and force fields used in molecular simulations, a general method for the assessment of the sampling quality is needed. Statistical mechanics principles suggest the populations of physical states characterize equilibrium sampling in a fundamental way. We therefore develop an approach for analyzing the variances in state populations, which quantifies the degree of sampling in terms of the effective sample size (ESS). The ESS estimates the number of statistically independent configurations contained in a simulated ensemble. The method is applicable to both traditional dynamics simulations as well as more modern (e.g., multicanonical) approaches. Our procedure is tested in a variety of systems from toy models to atomistic protein simulations. We also introduce a simple automated procedure to obtain approximate physical states from dynamic trajectories: this allows sample-size estimation in systems for which physical states are not known in advance.