We propose a class of nonstationary processes that characterize varying directional associations in space and time for point-referenced data. Our construction places a prior over possible directional edges within sparse directed acyclic graphs (DAGs), 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 are motivated by spatiotemporal modeling of air pollutants in which a directed edge in a DAG represents a prevailing wind direction causing some associated covariance in the pollutants. We outline Bayesian hierarchical models embedding the resulting nonstationary BAGs and illustrate inferential and performance gains of our methods compared to existing alternatives. We analyze fine particulate matter in California with high-resolution data from low-cost air quality sensors. An R package is available on GitHub.

翻译：我们建议了一组非静止过程,这些过程在空间和时间的不同方向联系中具有特征,用于点参照数据; 我们的建筑工程在分散的定向环绕图(DAGs)中先于可能的方向边缘,在分散的定向环绕图(DAGs)中考虑到一个领域方向相关性模式的不确定性; 由此产生的一袋DAGs(BAGs)过程导致大量数据的可解释性、可变性、可伸缩性,因为包内有大量DAGs的宽度; 我们的动机是空气污染物的随机模型,其中DAG的定向边缘代表一种普遍的风向,造成某些相关的污染物的共变。 我们概述了将由此产生的非静止环绕入非静止环绕图(DAGs)的海湾等级模型,并说明了与现有替代品相比,我们方法的推断和性能收益。 我们用低成本空气质量传感器的高分辨率数据分析了加利福尼亚的微粒子物质。 在GitHub上有一个R包。