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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.
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Fixed rank kriging for very large spatial data sets
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Gaussian predictive process models for large spatial data sets
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Covariance tapering for likelihood-based estimation in large spatial datasets
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Memory efficient kernel approximation
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Limitations on low rank approximations for covariance matrices of spatial data
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Fast direct methods for gaussian processes
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Sparse inverse covariance estimation with hierarchical matrices
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Hierarchical nearest-neighbor Gaussian process models for large geostatistical datasets
A. Datta, S. Banerjee, A. O. Finley, and A. E. Gelfand · 2015
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Does non-stationary spatial data always require non-stationary random fields?
G.-A. Fuglstad, D. Simpson, F. Lindgren, and H. Rue · 2015
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Application of hierarchical matrices for computing the Karhunen–Loève expansion
B. N. Khoromskij, A. Litvinenko, and H. G. Matthies · 2009
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Sparse data representation of random fields
A. Litvinenko and H. G. Matthies · 2009
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Y. Sun and M. G. Genton · 2011
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A matrix-free approach for solving the parametric Gaussian process maximum likelihood problem
M. Anitescu, J. Chen, and L. Wang · 2012
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Parametric and uncertainty computations with tensor product representations
H. Matthies, A. Litvinenko, O. Pajonk, B. V. Rosić, and E. Zander · 2012
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O. Pajonk, B. V. Rosić, A. Litvinenko, and H. G. Matthies · 2012
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Gaussian Processes , pages 15–108
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Efficient computation of Gaussian likelihoods for stationary Markov random field models
J. Guinness and I. Ipsen · 2015
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Hierarchical matrices: Algorithms and Analysis , volume 49 of Springer Series in Comp. Math
W. Hackbusch · 2015
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Efficient approximation of random fields for numerical applications
H. Harbrecht, M. Peters, and M. Siebenmorgen · 2015
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Hierarchical interpolative factorization for elliptic operators: differential equations
K. L. Ho and L. Ying · 2015
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Equivalent kriging
W. Kleiber and D. W. Nychka · 2015
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A multiresolution Gaussian process model for the analysis of large spatial datasets
D. Nychka, S. Bandyopadhyay, D. Hammerling, F. Lindgren, and S. Sain · 2015
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Fast computation of uncertainty quantification measures in the geostatistical approach to solve inverse problems
A. Saibaba and P. Kitanidis · 2015
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On the spectral equivalence of hierarchical matrix preconditioners for elliptic problems
M. Bebendorf, M. Bollhöfer, and M. Bratsch · 2016
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Multi-Level Restricted Maximum Likelihood Covariance Estimation and Kriging for Large Non-Gridded Spatial Datasets
J. E. Castrillon, M. G. Genton, and R. Yokota · 2016
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Statistically and computationally efficient estimating equations for large spatial datasets
Y. Sun and M. L. Stein · 2016
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Circulant embedding of approximate covariances for inference from gaussian data on large lattices
J. Guinness and M. Fuentes · 2017
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