Statistical Methods for Investigation of Heterogeneous Diffusion in Single-Particle Tracking

This paper presents a statistical approach to analyzing heterogeneous diffusion in single-particle tracking experiments, developed for the 2nd Anomalous Diffusion (AnDi) Challenge. Our method leverages the exponential distribution of squared displacements in two-dimensional fractional Brownian motion to identify and classify different diffusion models. We employ the Anderson-Darling test, Gaussian mixture models, and histogram analysis of sliding window medians to effectively segment trajectories and detect change points. Our approach showed competitive results in the 2nd AnDi challenge, ranking 4th in accuracy of change point determination and 5th in Jaccard similarity coefficient. We demonstrate the superiority of using median values over means in sliding windows for change point detection. This work contributes to the field of bioinformatics by providing robust statistical tools for anomalous diffusion studies in live cell membranes, offering a foundation upon which neural network approaches can be further developed and evaluated.