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DY: Fachverband Dynamik und Statistische Physik

DY 56: Brownian Motion and Anomalous Diffusion

DY 56.2: Talk

Friday, March 31, 2023, 09:45–10:00, ZEU 160

Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime — •Rick Bebon and Aljaz Godec — Max Planck Institute for Multidisciplinary Sciences, Göttingen, Germany

First-passage phenomena are ubiquitous in nature and are at the heart of, e.g. reaction kinetics, cell signaling, gene regulation, foraging behavior of animals, and stock option dynamics. Whereas theoretical studies typically focus on predicting statistics for a given process, practical applications often aim at inferring, e.g. mean first-passage times (i.e. inverse kinetic rates) from experimental or simulation data. The inference of mean first-passage times is challenging because only a small number of realizations is usually available, in turn leading to high uncertainties and non-Gaussian errors. We derive universal concentration inequalities for first-passage times of ergodic reversible Markov processes on discrete and continuous-state spaces. For a sample of n ≥ 1 independent realizations of the first-passage process, we prove a Cramér-Chernoff-type bound on the probability that the inferred sample mean deviates from the true mean first-passage time by more than any given amount. We further construct reliable non-asymptotic estimation guarantees, such as confidence intervals valid for all sample sizes n. Our findings allow for a rigorous uncertainty quantification of inferred first-passage times and lay grounds for a systematic understanding of finite-sample effects avoiding asymptotic approximations or biases due to prior-distribution assumptions.