Bayesian nonstationary spatial modeling for very large datasets

• Verfasst von: Katzfuß, Matthias [VerfasserIn]
• Titel: Bayesian nonstationary spatial modeling for very large datasets
• Verf.angabe: Matthias Katzfuss
• E-Jahr: 2013
• Jahr: 11 February 2013
• Umfang: 12 S.
• Teil: volume:24
• Teil: year:2013
• Teil: number:3
• Teil: pages:189-200
• Teil: extent:12
• Fussnoten: Gesehen am 22.04.2021
• Titel Quelle: Enthalten in: Environmetrics
• Ort Quelle: Chichester, West Sussex : Wiley, 1991
• Jahr Quelle: 2013
• Band/Heft Quelle: 24(2013), 3, Seite 189-200
• ISSN Quelle: 1099-095X
• DOI: doi:10.1002/env.2200
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: covariance tapering
• Sach-SW: full-scale approximation
• Sach-SW: low-rank models
• Sach-SW: massive datasets
• Sach-SW: model selection
• Sach-SW: reversible-jump MCMC
• K10plus-PPN: 1755736932

Abstract

With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles, and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial datasets observed on large spatial domains. Statistical analyses of such datasets provide two main challenges: first, traditional spatial-statistical techniques are often unable to handle large numbers of observations in a computationally feasible way; second, for large and heterogeneous spatial domains, it is often not appropriate to assume that a process of interest is stationary over the entire domain. We address the first challenge by using a model combining a low-rank component, which allows for flexible modeling of medium-to-long-range dependence via a set of spatial basis functions, with a tapered remainder component, which allows for modeling of local dependence using a compactly supported covariance function. Addressing the second challenge, we propose two extensions to this model that result in increased flexibility: first, the model is parameterized on the basis of a nonstationary Matérn covariance, where the parameters vary smoothly across space; second, in our fully Bayesian model, all components and parameters are considered random, including the number, locations, and shapes of the basis functions used in the low-rank component. Using simulated data and a real-world dataset of high-resolution soil measurements, we show that both extensions can result in substantial improvements over the current state-of-the-art. Copyright © 2013 John Wiley & Sons, Ltd.