  State-of-the-art techniques in passive particle-tracking microscopy provide
high-resolution path trajectories of diverse foreign particles in biological
fluids. For particles on the order of 1 micron diameter, these paths are
generally inconsistent with simple Brownian motion. Yet, despite an abundance
of data confirming these findings and their wide-ranging scientific
implications, stochastic modeling of the complex particle motion has received
comparatively little attention. Even among posited models, there is virtually
no literature on likelihood-based inference, model comparisons, and other
quantitative assessments. In this article, we develop a rigorous and
computationally efficient Bayesian methodology to address this gap. We analyze
two of the most prevalent candidate models for 30 second paths of 1 micron
diameter tracer particles in human lung mucus: fractional Brownian motion (fBM)
and a Generalized Langevin Equation (GLE) consistent with viscoelastic theory.
Our model comparisons distinctly favor GLE over fBM, with the former describing
the data remarkably well up to the timescales for which we have reliable
information.
