Spherical Process Models for Global Spatial Statistics

Handle URI:
http://hdl.handle.net/10754/626285
Title:
Spherical Process Models for Global Spatial Statistics
Authors:
Jeong, Jaehong; Jun, Mikyoung; Genton, Marc G. ( 0000-0001-6467-2998 )
Abstract:
Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Jeong J, Jun M, Genton MG (2017) Spherical Process Models for Global Spatial Statistics. Statistical Science 32: 501–513. Available: http://dx.doi.org/10.1214/17-sts620.
Publisher:
Institute of Mathematical Statistics
Journal:
Statistical Science
KAUST Grant Number:
OSR-2015-CRG4-2640
Issue Date:
28-Nov-2017
DOI:
10.1214/17-sts620
Type:
Article
ISSN:
0883-4237
Sponsors:
This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No: OSR-2015-CRG4-2640.
Additional Links:
https://projecteuclid.org/euclid.ss/1511838025
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorJeong, Jaehongen
dc.contributor.authorJun, Mikyoungen
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2017-12-05T06:12:00Z-
dc.date.available2017-12-05T06:12:00Z-
dc.date.issued2017-11-28en
dc.identifier.citationJeong J, Jun M, Genton MG (2017) Spherical Process Models for Global Spatial Statistics. Statistical Science 32: 501–513. Available: http://dx.doi.org/10.1214/17-sts620.en
dc.identifier.issn0883-4237en
dc.identifier.doi10.1214/17-sts620en
dc.identifier.urihttp://hdl.handle.net/10754/626285-
dc.description.abstractStatistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.en
dc.description.sponsorshipThis publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No: OSR-2015-CRG4-2640.en
dc.publisherInstitute of Mathematical Statisticsen
dc.relation.urlhttps://projecteuclid.org/euclid.ss/1511838025en
dc.rightsArchived with thanks to Statistical Scienceen
dc.subjectAxial symmetryen
dc.subjectchordal distanceen
dc.subjectgeodesic distanceen
dc.subjectnonstationarityen
dc.subjectsmoothnessen
dc.subjectsphereen
dc.titleSpherical Process Models for Global Spatial Statisticsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalStatistical Scienceen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Statistics, Texas A&M University, College Station, Texas 77843-3143, USAen
kaust.authorJeong, Jaehongen
kaust.authorGenton, Marc G.en
kaust.grant.numberOSR-2015-CRG4-2640en
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