  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.
