Bag of DAGs: Inferring Directional Dependence in Spatiotemporal Processes

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.