Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets

Handle URI:
http://hdl.handle.net/10754/625430
Title:
Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets
Authors:
Litvinenko, Alexander ( 0000-0001-5427-3598 ) ; Sun, Ying ( 0000-0001-6703-4270 ) ; Genton, Marc G. ( 0000-0001-6467-2998 ) ; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, since H-matrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Issue Date:
3-Sep-2017
Type:
Technical Report
Sponsors:
KAUST
Appears in Collections:
Technical Reports

Full metadata record

DC FieldValue Language
dc.contributor.authorLitvinenko, Alexanderen
dc.contributor.authorSun, Yingen
dc.contributor.authorGenton, Marc G.en
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2017-09-10T07:20:38Z-
dc.date.available2017-09-10T07:20:38Z-
dc.date.issued2017-09-03-
dc.identifier.urihttp://hdl.handle.net/10754/625430-
dc.description.abstractWe use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, since H-matrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.en
dc.description.sponsorshipKAUSTen
dc.subjectComputational statisticsen
dc.subjecthierarchical matriesen
dc.subjectlarge datasetsen
dc.subjectMatern covarianceen
dc.subjectRandom fielden
dc.subjectparameter identificationen
dc.subjectspatial statisticsen
dc.titleLikelihood Approximation With Hierarchical Matrices For Large Spatial Datasetsen
dc.typeTechnical Reporten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
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