  A series of experiments in stationary and moving passenger rail cars were
conducted to measure removal rates of particles in the size ranges of
SARS-CoV-2 viral aerosols, and the air changes per hour provided by existing
and modified air handling systems. Such methods for exposure assessments are
customarily based on mechanistic models derived from physical laws of particle
movement that are deterministic and do not account for measurement errors
inherent in data collection. The resulting analysis compromises on reliably
learning about mechanistic factors such as ventilation rates, aerosol
generation rates and filtration efficiencies from field measurements. This
manuscript develops a Bayesian state space modeling framework that synthesizes
information from the mechanistic system as well as the field data. We derive a
stochastic model from finite difference approximations of differential
equations explaining particle concentrations. Our inferential framework trains
the mechanistic system using the field measurements from the chamber
experiments and delivers reliable estimates of the underlying physical process
with fully model-based uncertainty quantification. Our application falls within
the realm of Bayesian "melding" of mechanistic and statistical models and is of
significant relevance to industrial hygienists and public health researchers
working on assessment of exposure to viral aerosols in rail car fleets.
