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Gaussian random fields over infinite-dimensional Hilbert spaces require the definition of appropriate covariance operators.
Stochastic-processes in several dimensions
Peter Whittle · 1963
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On a system of two-dimensional recurrence equations
Julian Besag · 1981
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Aristotelian prior boundary conditions
Daniela Calvetti, Jari P Kaipio, and Erkki Somersalo · 2006
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An Introduction to Infinite-dimensional Analysis
Giuseppe Da Prato · 2006
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Approximate Bayesian inference for hierarchical Gaussian Markov random field models
Hvard Rue and Sara Martino · 2007
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An estimator for the diagonal of a matrix
Costas Bekas, Effrosyni Kokiopoulou, and Yousef Saad · 2007
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Introduction to Stochastic PDEs
Martin Hairer · 2009
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Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems
Lin Lin, Jianfeng Lu, Lexing Ying, Roberto Car, and Weinan E · 2009
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Low cost high performance uncertainty quantification
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Inverse problems: A Bayesian perspective
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NIST Handbook of Mathematical Functions
F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, editors · 2010
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An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach
Finn Lindgren, Hvard Rue, and Johan Lindström · 2011
Think continuous: Markovian Gaussian models in spatial statistics
Daniel Simpson, Finn Lindgren, and Hvard Rue · 2012
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A probing method for computing the diagonal of a matrix inverse
Jok M. Tang and Yousef Saad · 2012
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Automated Solution of Differential Equations by the Finite Element Method
Anders Logg, Kent-Andre Mardal, and Garth N. Wells, editors · 2012
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A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion
Tan Bui-Thanh, Omar Ghattas, James Martin, and Georg Stadler · 2013
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Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography
Lassi Roininen, Janne M. J. Huttunen, and Sari Lasanen · 2014
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In order to make spatial statistics computationally feasible, we need to forget about the covariance function
Daniel Simpson, Finn Lindgren, and Hvard Rue · 2012
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Cubature—Adaptive Multi-dimension Integration
Steven G. Johnson
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Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet
Tobin Isaac, Noemi Petra, Georg Stadler, and Omar Ghattas · 2015
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http://dlmf.nist.gov/ , Release 1.0.10 of 2015-08-07
NIST Digital Library of Mathematical Functions · 2015
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