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Activity Number: 131 - Methods for Spatial, Temporal, and Spatio-Temporal Data
Type: Contributed
Date/Time: Monday, August 9, 2021 : 1:30 PM to 3:20 PM
Sponsor: Section on Statistics and the Environment
Abstract #318297
Title: Bag of DAGs: Flexible and Scalable Modeling of Spatiotemporal Dependence
Author(s): Bora Jin* and Michele Peruzzi and James Johndrow and David Dunson
Companies: Duke University and Duke University and University of Pennsylvania and Duke University
Keywords: Air pollution; Directed acyclic graphs; Nonstationary covariance; Scalable Gaussian process; Spatiotemporal; Wind directions

We propose a computationally efficient approach to construct nonstationary covariance structures for Gaussian processes (GPs) in point-referenced geostatistical models. Current methods that impose nonstationarity on the covariance functions often suffer from computational bottlenecks, causing researchers to choose less appropriate alternatives in many applications. A main contribution of this paper is the development of a well-defined spatial process with the nonstationary covariance using multiple yet simple directed acyclic graphs (DAGs), leading to computational efficiency, flexibility, and interpretability. Inspired by graph-based approaches, we use a “bag of DAGs,” each of which is chosen to represent a different possible dependence structure. Combined with a domain partitioning idea from the scalable GP literature, our methods enjoy efficient computations. We are motivated by spatiotemporal modelling of air pollutants in which a DAG represents a prevailing wind direction causing some associated covariance in the pollutants. We establish Bayesian hierarchical models embedding the nonstationary GP and analyze spatiotemporal variability of fine particulate matter (PM2.5).

Authors who are presenting talks have a * after their name.

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