State-of-the-art techniques in passive particle-tracking microscopy provide high-resolution path trajectories of diverse foreign particles in biological fluids. In order to analyze experiments often tracking thousands of particles at once, scientists must account for many sources of unwanted variability, such as heterogeneity of the fluid environment and measurement error. To this end, this talk presents a versatile family of hierarchical stochastic process models, along with a scalable split-merge distributed computing strategy for parameter inference. Also presented are several applications to quantifying subdiffusive mobility of tracer particles in human lung mucus.