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A series of experiments in stationary and moving passenger rail cars wereconducted to measure removal rates of particles in the size ranges ofSARS-CoV-2 viral aerosols, and the air changes per hour provided by existingand modified air handling systems. Such methods for exposure assessments arecustomarily based on mechanistic models derived from physical laws of particlemovement that are deterministic and do not account for measurement errorsinherent in data collection. The resulting analysis compromises on reliablylearning about mechanistic factors such as ventilation rates, aerosolgeneration rates and filtration efficiencies from field measurements. Thismanuscript develops a Bayesian state space modeling framework that synthesizesinformation from the mechanistic system as well as the field data. We derive astochastic model from finite difference approximations of differentialequations explaining particle concentrations. Our inferential framework trainsthe mechanistic system using the field measurements from the chamberexperiments and delivers reliable estimates of the underlying physical processwith fully model-based uncertainty quantification. Our application falls withinthe realm of Bayesian ``melding'' of mechanistic and statistical models and isof significant relevance to environmental hygienists and public healthresearchers working on assessing performance of aerosol removal rates for railcar fleets.

Bayesian Hierarchical Modeling and Inference for Mechanistic Systems in Industrial Hygiene