title: Bayesian modeling and analysis for gradients in spatiotemporal processes.
abstract: Stochastic process models are widely employed for analyzing spatiotemporal datasets in various scientific disciplines including, but not limited to, environmental monitoring, ecological systems, forestry, hydrology, meteorology, and public health. After inferring on a spatiotemporal process for a given dataset, inferential interest may turn to estimating rates of change, or gradients, over space and time. This manuscript develops fully model-based inference on spatiotemporal gradients under continuous space, continuous time settings. Our contribution is to offer, within a flexible spatiotemporal process model setting, a framework to estimate arbitrary directional gradients over space at any given timepoint, temporal derivatives at any given spatial location and, finally, mixed spatiotemporal gradients that reflect rapid change in spatial gradients over time and vice-versa. We achieve such inference without compromising on rich and flexible spatiotemporal process models and use nonseparable covariance structures. We illustrate our methodology using a simulated data example and subsequently apply it to a dataset of daily PM2.5 concentrations in California, where the spatiotemporal gradient process reveals the effects of California's unique topography on pollution and detects the aftermath of a devastating series of wildfires.
authors.affiliation: Division of Heart Disease and Stroke Prevention, NCCDPHP/CDC, Atlanta, Georgia 30341-3717, U.S.A.
authors.forename: Harrison
authors.initials: H
authors.lastname: Quick
authors.affiliation: Department of Biostatistics, University of California, Los Angeles, California 90095-1772, U.S.A.
authors.forename: Sudipto
authors.initials: S
authors.lastname: Banerjee
authors.affiliation: Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.
authors.forename: Bradley P
authors.initials: BP
authors.lastname: Carlin
mesh_terms: D000397:Air Pollution / Q000032:analysis / Q000706:statistics & numerical data*; D001499:Bayes Theorem; D002140:California; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005390:Fires / Q000706:statistics & numerical data*; D006801:Humans; D015233:Models, Statistical; D052638:Particulate Matter / Q000032:analysis*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D062211:Spatio-Temporal Analysis
chemical_list: D052638:Particulate Matter
keywords: Gaussian process; Gradients; Markov chain Monte Carlo