Bag of DAGs: Inferring Directional Dependence in Spatiotemporal Processes.

Area of Science:

• Environmental Science
• Statistics
• Data Science

Background:

• Spatiotemporal modeling of air pollutants is crucial for understanding environmental health impacts.
• Local wind patterns significantly influence pollutant dispersion, but directional data can be incomplete or unreliable.
• Existing methods may struggle with the complexity and scale of high-resolution air quality data.

Purpose of the Study:

• To develop a novel statistical framework for characterizing space- and time-varying directional associations in point-referenced environmental data.
• To address challenges posed by missing or uncertain information on prevailing wind directions in air pollution modeling.
• To introduce a scalable and interpretable method for analyzing complex spatiotemporal environmental data.

Main Methods:

• Proposed a class of nonstationary processes termed Bag of DAGs processes (BAGs).
• Mapped discrete wind directions to edges in sparse directed acyclic graphs (DAGs) to model directional correlations.
• Developed Bayesian hierarchical models incorporating BAGs for robust inference.

Main Results:

• Demonstrated interpretable nonstationarity and scalability for large datasets due to the sparsity of DAGs.
• Showcased inferential and performance gains compared to state-of-the-art spatiotemporal modeling techniques.
• Successfully analyzed fine particulate matter data from California's 2020 wildfire season using high-resolution sensor data.

Conclusions:

• Bag of DAGs processes provide a flexible and powerful tool for spatiotemporal environmental data analysis, particularly when directional dependencies are complex.
• The method enhances understanding of pollutant transport by effectively handling uncertainty in wind direction data.
• The developed R package facilitates the application of these advanced statistical methods in environmental research.