Show simple item record

dc.contributor.authorGenton, Marc G.
dc.contributor.authorKleiber, William
dc.date.accessioned2015-08-03T12:34:46Z
dc.date.available2015-08-03T12:34:46Z
dc.date.issued2015-05
dc.identifier.citationGenton, M. G., & Kleiber, W. (2015). Cross-Covariance Functions for Multivariate Geostatistics. Statistical Science, 30(2), 147–163. doi:10.1214/14-sts487
dc.identifier.issn08834237
dc.identifier.doi10.1214/14-STS487
dc.identifier.urihttp://hdl.handle.net/10754/564165
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.
dc.publisherInstitute of Mathematical Statistics
dc.subjectAsymmetry
dc.subjectCo-kriging
dc.subjectMultivariate random fields
dc.subjectNonstationarity
dc.subjectSeparability
dc.subjectSmoothness
dc.subjectSpatial statistics
dc.subjectSymmetry
dc.titleCross-covariance functions for multivariate geostatistics
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentSpatio-Temporal Statistics and Data Analysis Group
dc.contributor.departmentStatistics Program
dc.identifier.journalStatistical Science
dc.contributor.institutionDepartment of Applied Mathematics, University of Colorado, BoulderCO, United States
dc.identifier.arxivid1507.08017
kaust.personGenton, Marc G.


This item appears in the following Collection(s)

Show simple item record