We propose a computationally efficient approach to construct a class of nonstationary spatiotemporal processes in point-referenced geostatistical models. Current methods that impose nonstationarity directly on covariance functions of Gaussian processes (GPs) often suffer from computational bottlenecks, causing researchers to choose less appropriate alternatives in many applications. A main contribution of this paper is the development of a well-defined nonstationary process using multiple yet simple directed acyclic graphs (DAGs), which leads to computational efficiency, flexibility, and interpretability. Rather than acting on the covariance functions, we induce nonstationarity via sparse DAGs across domain partitions, whose edges are interpreted as directional correlation patterns in space and time. We account for uncertainty about these patterns by considering local mixtures of DAGs, leading to a ``bag of DAGs'' approach. We are motivated by spatiotemporal modeling of air pollutants in which a directed edge in DAGs represents a prevailing wind direction causing some associated covariance in the pollutants; for example, an edge for northwest to southeast winds. We establish Bayesian hierarchical models embedding the resulting nonstationary process from the bag of DAGs approach and illustrate inferential and performance gains of the methods compared to existing alternatives. We consider a novel application focusing on the analysis of fine particulate matter (PM2.5) in South Korea and the United States. The code for all analyses is publicly available on Github.
翻译:我们建议采用一种计算效率高的方法,在点参照的地理统计模型中建立一类非静止的时空过程。目前,直接将不常态直接强加于高西进程(GPs)共变量功能的方法经常受到计算瓶颈的影响,研究人员在许多应用中选择了不适当的替代品。本文的主要贡献是利用多种简单定向的循环图(DAGs)来开发一个定义明确的非静态过程,从而实现计算效率、灵活性和可解释性。我们不是根据共变功能采取行动,而是通过分散的DAGs在域际分区中引起不常态,其边缘被解释为空间和时间的定向相关模式。我们通过考虑本地的DAGs混合物来解释这些模式的不确定性,从而导致DAGs方法的“一袋式”。我们受到空气污染的广度模型的驱动,DAGs的定向边缘代表着一种普遍的风向,导致污染物的某些相关差异;例如,在西北至东南的DAG中,其边缘被解释为空间和时间的定向关联性关系。我们将这些模式的不确定性用于在GAGsalian系统中的升级分析。我们把现有等级模型用于分析。