Understanding the sources that contribute to fine particulate matter (PM$_{2.5}$) is of crucial importance for designing and implementing targeted air pollution mitigation strategies. Determining what factors contribute to a pollutant's concentration goes under the name of source apportionment and it is a problem long studied by atmospheric scientists and statisticians alike. In this paper, we propose a Bayesian model for source apportionment, that advances the literature on source apportionment by allowing estimation of the number of sources and accounting for spatial and temporal dependence in the observed pollutants' concentrations. Taking as example observations of six species of fine particulate matter observed over the course of a year, we present a latent functional factor model that expresses the space-time varying observations of log concentrations of the six pollutant as a linear combination of space-time varying emissions produced by an unknown number of sources each multiplied by the corresponding source's relative contribution to the pollutant. Estimation of the number of sources is achieved by introducing source-specific shrinkage parameters. Application of the model to simulated data showcases its ability to retrieve the true number of sources and to reliably estimate the functional latent factors, whereas application to PM$_{2.5}$ speciation data in California identifies 3 major sources for the six PM$_{2.5}$ species.

翻译：理解细颗粒物（PM$_{2.5}$）的来源对于设计和实施有针对性的空气污染缓解策略至关重要。确定影响污染物浓度的因素被称为源解析，这是大气科学家和统计学家长期研究的问题。本文提出了一种用于源解析的贝叶斯模型，该模型通过允许估计源的数量并考虑观测污染物浓度的时空依赖性，推动了源解析领域的研究进展。以一年内观测到的六种细颗粒物物种为例，我们提出了一个潜在函数因子模型，该模型将六种污染物对数浓度的时空变化观测值表达为未知数量的源所产生的时空变化排放的线性组合，每个排放乘以相应源对污染物的相对贡献。通过引入源特定的收缩参数来实现对源数量的估计。将该模型应用于模拟数据展示了其恢复真实源数量并可靠估计潜在函数因子的能力，而在加利福尼亚州PM$_{2.5}$物种数据中的应用识别出六种PM$_{2.5}$物种的3个主要来源。