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，用于刻画点参照数据中随空间和时间变化的方向关联特征。研究动机源于空气污染物的时空建模，其中局部风型是污染物扩散的关键决定因素，但主导风向信息可能缺失或不可靠。我们将离散的风向集合映射至稀疏有向无环图（DAG）中的边，从而对区域内方向相关模式的不确定性进行建模。由此产生的DAG集合过程（BAGs）因集合中DAG的稀疏性而具有可解释的非平稳性与大规模数据可扩展性。我们概述了基于BAGs的贝叶斯层次模型，并展示了该方法相较于其他前沿替代方案在推断与性能上的优势。基于2020年加州 wildfire 季节低成本空气质量传感器的高分辨率数据，我们分析了细颗粒物污染。相关R包已发布于GitHub。