Bayesian Spatiotemporal Wombling

• 成果类型: Article; Early Access
• 署名作者: Halder, Aritra; Li, Didong; Banerjee, Sudipto
• 署名单位: Drexel University; University of North Carolina; University of North Carolina Chapel Hill; University of California System; University of California Los Angeles
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2700798
• 发表日期: 2026-09-01
• 关键词: Gaussian processes; Parametric surfaces; Rates of change; Spatiotemporal boundary analysis; Spatiotemporal processes; Wombling; SMOOTHNESS PROPERTIES; gradients; derivatives; rates

摘要

Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed continuously over time) at arbitrary space-time coordinates, scientific interest often turns to gleaning information regarding zones of rapid spatial-temporal change. We develop Bayesian modeling and inference for directional rates of change along a given surface. These surfaces, which demarcate regions of rapid change, are referred to as wombling surface boundaries. Existing methods for studying such changes have often been associated with curves and are not easily extendable to surfaces resulting from curves evolving over time. Our current contribution devises a fully model-based inferential framework for analyzing differential behavior in spatiotemporal responses by formalizing the notion of a wombling surface boundary using conventional multi-linear vector analytic frameworks and geometry followed by posterior predictive computations using triangulated surface approximations. We illustrate our methodology with comprehensive simulation experiments followed by multiple applications in neuroimaging; environmental and climate science and pollutant analysis in environmental health. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.