Bag of DAGs: Inferring Directional Dependence in Spatiotemporal Processes

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.