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 environmental hygienists and public health researchers working on assessing performance of aerosol removal rates for rail car fleets.

翻译：为测量SARS-CoV-2病毒气溶胶粒径范围内的颗粒去除率，以及现有及改进型空气处理系统每小时换气次数，在静止和移动的客运铁路车厢中开展了一系列实验。此类暴露评估方法通常基于源自颗粒运动物理定律的确定性机械模型，该模型不考虑数据采集中固有的测量误差。由此得到的分析结果在从现场测量中可靠提取通风速率、气溶胶生成速率和过滤效率等机械因素方面存在局限。本文提出一种贝叶斯状态空间建模框架，该框架综合了来自机械系统及现场数据的信息。我们通过解释颗粒浓度的微分方程有限差分近似推导出随机模型。我们的推断框架利用实验舱测量的现场数据训练机械系统，基于完整模型的不确定性量化，提供对潜在物理过程的可靠估计。本应用属于机械模型与统计模型的贝叶斯"融合"范畴，对于从事铁路车队气溶胶去除率性能评估工作的环境卫生学家和公共卫生研究人员具有重要参考价值。