Error Breakdown and Sensitivity Analysis of Dynamical Quantities in Markov State Models

Abstract: Markov state models (MSMs) are widely employed to analyze the kinetics of complex systems. But despite their effectiveness in many applications, MSMs are prone to systematic or statistical errors, often exacerbated by suboptimal hyperparameter choice. In this paper, we attempt to understand how these choices affect the error of estimates of mean first-passage times and committors, key quantities in chemical rate theory. We first evaluate the performance of the recently introduced "stopped-process estimator" that attempts to reduce error caused by choosing a too-large lag time. We then study the effect of statistical errors on Markov state model construction using the condition number, which measures an MSM's sensitivity to perturbation. This analysis helps give an intuition into which factors cause an MSM to be more or less sensitive to statistical error. Our work highlights the importance of choosing a good sampling measure, the measure from which the initial points are drawn, and has implications for recent work applying a variational principle for evaluating the committor.