Optimal estimators and asymptotic variances for nonequilibrium path-ensemble averages

Abstract

Existing optimal estimators of nonequilibrium path-ensemble averages are shown to fall within the framework of extended bridge sampling. Using this framework, we derive a general minimal-variance estimator that can combine nonequilibrium trajectory data sampled from multiple path-ensembles to estimate arbitrary functions of nonequilibrium expectations. The framework is also applied to obtaining asymptotic variance estimates, which are a useful measure of statistical uncertainty. In particular, we develop asymptotic variance estimates pertaining to Jarzynski's equality for free energies and the Hummer-Szabo expressions for the potential of mean force, calculated from uni- or bidirectional path samples. Lastly, they are demonstrated on a model single-molecule pulling experiment. In these simulations, the asymptotic variance expression is found to accurately characterize the confidence intervals around estimators when the bias is small. Hence, it does not work well for unidirectional estimates with large bias, but for this model it largely reflects the true error in a bidirectional estimator derived by Minh and Adib.

9 pages, 4 figures, 2 appendicies

References in corpus (11)

• Optimal finite-time processes in stochastic thermodynamics
• Rare events and the convergence of exponentially averaged work values
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• Optimized free energies from bidirectional single-molecule force spectroscopy
• Computing the optimal protocol for finite-time processes in stochastic thermodynamics
• Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise
• Recovery of free energy branches in single molecule experiments
• Optimal estimates of free energies from multi-state nonequilibrium work data
• Annealed importance sampling of dileucine peptide
• Optimum bias for fast-switching free energy calculations
• Density-Dependent Analysis of Nonequilibrium Paths Improves Free Energy Estimates

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