(103g) Ordinary Least Squares, Extraordinary Overconfidence: Towards Improved Statistical Estimators for Particle Diffusivity

Self-diffusivity and binary diffusivity are fundamental transport properties of interest in both molecular simulations and single-particle tracking experiments. Given an ensemble of particle trajectories, it is often the case in practice that an estimate of the diffusivity (and its associated uncertainty) is obtained by fitting a line to mean squared displacement data via ordinary least squares, based on the classic results of Einstein and Smoluchowski. In this work, we discuss why this procedure is statistically suboptimal and demonstrate how improved statistical procedures — both Bayesian and frequentist — can instead be applied to particle position data in order to estimate diffusivities with statistically rigorous uncertainties / error bars. Applications to simulations of bulk and nanoconfined fluids as well as nanoparticle single-particle tracking data will also be discussed.