Bayesian Hierarchical Modeling and Inference for Mechanistic Systems in Industrial Hygiene

TL;DR

This paper introduces a Bayesian hierarchical modeling approach that combines mechanistic particle transport models with field data to improve the accuracy and uncertainty quantification in aerosol exposure assessments in rail cars.

Contribution

It develops a Bayesian state space framework that integrates physical laws with measurement data, enabling more reliable inference of ventilation and filtration parameters.

Findings

Reliable estimates of ventilation and filtration rates from field data.

Quantification of uncertainty in particle concentration models.

Enhanced understanding of aerosol dynamics in rail environments.

Abstract

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.