Uncertainty Estimation

Abstract

Markov models provide a useful simplified representation for characterizing the long-time statistical evolution of biomolecules in a manner that allows direct comparison with experiments as well as the elucidation of mechanistic pathways for an inherently stochastic process. A vital part of meaningful comparison with experiment is the characterization of the statistical uncertainty in the predicted experimental measurement, which may take the form of an equilibrium measurement of some spectroscopic signal, the time-evolution of this signal following a perturbation, or the observation of some statistic such as the correlation function of the equilibrium dynamics of a single molecule. Without meaningful error bars which arise from both approximation and statistical error, there is no way to determine whether the deviations between model and experiment are statistically meaningful. In this chapter, we describe several approaches for computing statistical uncertainty of the estimated transition matrix and quantities calculated from it.

Reprinted with permission from Prinz et al. (Markov models of molecular kinetics: Generation and validation. J. Chem. Phys. 134:174,105, 2011), Noé (Probability Distributions of Molecular Observables computed from Markov Models. J Chem Phys 128:244,103, 2008), Chodera and Noé (Probability distributions of molecular observables computed from Markov models. ii: Uncertainties in observables and their time-evolution. J Chem Phys 133:105,102, 2010). Copyright 2008, 2010, 2011, American Institute of Physics.