Frequentist and Bayesian Approaches to Error Estimation in Particle-Based Simulations of Soft Matter Transport

Particle-based dynamics (e.g., molecular dynamics, Brownian dynamics, etc.) are used extensively to study transport phenomena in soft matter. In this talk, we describe several recent statistical results governing the quantification of uncertainties associated with the analysis of data from particle-based simulations, both within a frequentist framework and within a Bayesian framework. Using diffusion as measured via the Einstein relation as a case study, we show that commonplace statistical estimators (based upon, e.g., ordinary-least-squares regression) yield substantial and systematic discrepancies for variances of transport quantities, when compared to large-scale/long-time simulations. We present two computationally efficient schemes that can improve error estimates, thereby establishing more credible confidence estimates for particle-based simulations of soft matter transport phenomena. We close by briefly discussing the implications for uncertainty quantification of transport measurements using linear-response-theory-based approaches (e.g., Green-Kubo relations).