Likelihood approximation with hierarchical matrices for large spatial datasets
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ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionStatistics Program
Applied Mathematics and Computational Science Program
Extreme Computing Research Center
Date
2019-02-12Preprint Posting Date
2017-09-08Online Publication Date
2019-02-12Print Publication Date
2019-09Permanent link to this record
http://hdl.handle.net/10754/625430
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The unknown parameters (variance, smoothness, and covariance length) of a spatial covariance function can be estimated by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, the discretized covariance function is approximated in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and O(knlogn) storage, where the rank k is a small integer, and n is the number of locations. The H-matrix technique can approximate general covariance matrices (also inhomogeneous) discretized on a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse has to be sparse. It is investigated how the H-matrix approximation error influences the estimated parameters. Numerical examples with Monte Carlo simulations, where the true values of the unknown parameters are given, and an application to soil moisture data with unknown parameters are presented. The C, C++ codes and data are freely available.Citation
Litvinenko, A. et al., 2019. Likelihood approximation with hierarchical matrices for large spatial datasets. Computational Statistics & Data Analysis, 137, pp.115–132. Available at: http://dx.doi.org/10.1016/j.csda.2019.02.002.Sponsors
The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). Additionally, we would like to express our special thanks of gratitude to Ronald Kriemann (for the HLIBPro software library) as well as to Lars Grasedyck and Steffen Börm for the HLIB software library. Alexander Litvinenko was supported by the Bayesian Computational Statistics & Modeling group (KAUST), the SRI-UQ group (KAUST), the Extreme Computing Research Center (KAUST), and the Alexander von Humboldt Foundation.Publisher
Elsevier BVarXiv
arXiv:1709.04419Additional Links
https://www.sciencedirect.com/science/article/pii/S0167947319300374ae974a485f413a2113503eed53cd6c53
10.1016/j.csda.2019.02.002
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Except where otherwise noted, this item's license is described as This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)