We propose a class of nonstationary processes to characterize space- and time-varying directional associations in point-referenced data. We are motivated by spatiotemporal modeling of air pollutants in which local wind patterns are key determinants of the pollutant spread, but information regarding prevailing wind directions may be missing or unreliable. We propose to map a discrete set of wind directions to edges in a sparse directed acyclic graph (DAG), accounting for uncertainty in directional correlation patterns across a domain. The resulting Bag of DAGs processes (BAGs) lead to interpretable nonstationarity and scalability for large data due to sparsity of DAGs in the bag. We outline Bayesian hierarchical models using BAGs and illustrate inferential and performance gains of our methods compared to other state-of-the-art alternatives. We analyze fine particulate matter using high-resolution data from low-cost air quality sensors in California during the 2020 wildfire season. An R package is available on GitHub.

翻译：我们提出一类非平稳过程来刻画点参考数据中随空间和时间变化的方向性关联。本研究受到空气污染物时空建模的启发，其中局部风场模式是污染物扩散的关键决定因素，但关于主导风向的信息可能存在缺失或不可靠。我们提出将离散的风向集合映射至稀疏有向无环图（DAG）的边，从而量化整个研究域内方向相关性模式的不确定性。由于图袋中DAG的稀疏性，所得到的有向无环图袋过程（BAGs）兼具可解释的非平稳性和适用于大规模数据的可扩展性。我们构建了基于BAGs的贝叶斯分层模型框架，并通过对比其他前沿方法，展示了本方法在推断性能和计算效率上的优势。我们利用2020年野火季期间加利福尼亚州低成本空气质量传感器的高分辨率数据，对细颗粒物进行了实证分析。相关R软件包已在GitHub平台发布。