TY - JOUR
T1 - Estimation of Spatial Deformation for Nonstationary Processes via Variogram Alignment
AU - Qadir, Ghulam A.
AU - Sun, Ying
AU - Kurtek, Sebastian
N1 - KAUST Repository Item: Exported on 2021-02-11
Acknowledged KAUST grant number(s): OSR-2019-CRG7-3800
Acknowledgements: The authors would like to thank the two reviewers, an associate editor, and the editor for constructive comments and helpful suggestions. The work is partially supported by King Abdullah University of Science and Technology (KAUST), Office of Sponsored Research (OSR) under Award No: OSR-2019-CRG7-3800, the National Science Foundation (NSF) grants: DMS-1613054, CCF-1740761, CCF-1839252, DMS-2015226, and the National Institutes of Health (NIH) grant: R37-CA214955.
PY - 2021/2/4
Y1 - 2021/2/4
N2 - In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence structure, therefore requiring nonstationary modeling. Spatial deformation is one of the main methods for modeling nonstationary processes, assuming the nonstationary process has a stationary counterpart in the deformed space. The estimation of the deformation function poses severe challenges. Here, we introduce a novel approach for nonstationary geostatistical modeling, using space deformation, when a single realization of the spatial process is observed. Our method is based on aligning regional variograms, where warping variability of the distance from each subregion explains the spatial nonstationarity. We propose to use multi-dimensional scaling to map the warped distances to spatial locations. We assess the performance of our new method using multiple simulation studies. Additionally, we illustrate our methodology on precipitation data to estimate the heterogeneous spatial dependence and to perform spatial predictions.
AB - In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence structure, therefore requiring nonstationary modeling. Spatial deformation is one of the main methods for modeling nonstationary processes, assuming the nonstationary process has a stationary counterpart in the deformed space. The estimation of the deformation function poses severe challenges. Here, we introduce a novel approach for nonstationary geostatistical modeling, using space deformation, when a single realization of the spatial process is observed. Our method is based on aligning regional variograms, where warping variability of the distance from each subregion explains the spatial nonstationarity. We propose to use multi-dimensional scaling to map the warped distances to spatial locations. We assess the performance of our new method using multiple simulation studies. Additionally, we illustrate our methodology on precipitation data to estimate the heterogeneous spatial dependence and to perform spatial predictions.
UR - http://hdl.handle.net/10754/660676
UR - https://www.tandfonline.com/doi/full/10.1080/00401706.2021.1883481
U2 - 10.1080/00401706.2021.1883481
DO - 10.1080/00401706.2021.1883481
M3 - Article
SN - 0040-1706
SP - 1
EP - 28
JO - Technometrics
JF - Technometrics
ER -