Bag of DAGs: Flexible Nonstationary Modeling of Spatiotemporal Dependence

We propose a class of nonstationary processes that characterize varying directional associations in space and time for point-referenced data. Our construction is based on local mixtures of sparse directed acyclic graphs (DAGs). In stochastically choosing DAG edges from a "bag," we account 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 all 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 (PM2.5) in California with high-resolution data from low-cost air quality sensors. The code for all analyses is publicly available at https://github.com/jinbora0720/BAG.