Cross-covariance functions for multivariate geostatistics

Handle URI:
http://hdl.handle.net/10754/564165
Title:
Cross-covariance functions for multivariate geostatistics
Authors:
Genton, Marc G. ( 0000-0001-6467-2998 ) ; Kleiber, William
Abstract:
Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Matérn and nonstationary and space-time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems. © Institute of Mathematical Statistics, 2015.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Spatio-Temporal Statistics and Data Analysis Group
Publisher:
Institute of Mathematical Statistics
Journal:
Statistical Science
Issue Date:
May-2015
DOI:
10.1214/14-STS487
Type:
Article
ISSN:
08834237
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGenton, Marc G.en
dc.contributor.authorKleiber, Williamen
dc.date.accessioned2015-08-03T12:34:46Zen
dc.date.available2015-08-03T12:34:46Zen
dc.date.issued2015-05en
dc.identifier.issn08834237en
dc.identifier.doi10.1214/14-STS487en
dc.identifier.urihttp://hdl.handle.net/10754/564165en
dc.description.abstractContinuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years, scientists developed models that aimed at capturing the spatial behavior for an individual process; only within the last few decades has it become commonplace to model multiple processes jointly. The key difficulty is in specifying the cross-covariance function, that is, the function responsible for the relationship between distinct variables. Indeed, these cross-covariance functions must be chosen to be consistent with marginal covariance functions in such a way that the second-order structure always yields a nonnegative definite covariance matrix. We review the main approaches to building cross-covariance models, including the linear model of coregionalization, convolution methods, the multivariate Matérn and nonstationary and space-time extensions of these among others. We additionally cover specialized constructions, including those designed for asymmetry, compact support and spherical domains, with a review of physics-constrained models. We illustrate select models on a bivariate regional climate model output example for temperature and pressure, along with a bivariate minimum and maximum temperature observational dataset; we compare models by likelihood value as well as via cross-validation co-kriging studies. The article closes with a discussion of unsolved problems. © Institute of Mathematical Statistics, 2015.en
dc.publisherInstitute of Mathematical Statisticsen
dc.subjectAsymmetryen
dc.subjectCo-krigingen
dc.subjectMultivariate random fieldsen
dc.subjectNonstationarityen
dc.subjectSeparabilityen
dc.subjectSmoothnessen
dc.subjectSpatial statisticsen
dc.subjectSymmetryen
dc.titleCross-covariance functions for multivariate geostatisticsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentSpatio-Temporal Statistics and Data Analysis Groupen
dc.identifier.journalStatistical Scienceen
dc.contributor.institutionDepartment of Applied Mathematics, University of Colorado, BoulderCO, United Statesen
kaust.authorGenton, Marc G.en
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