Covariance Tapering for Interpolation of Large Spatial Datasets

By Reinhard Furrer, Marc G. Genton, D. Nychka. 2006

775 citations recorded by the source corpus.

Subfields: Applied Mathematics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/b08b48008b9f4408074f9b113fe3d9d755644713

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In Applied Mathematics

In Environmental Engineering

Citations in the corpus

A class of Matérn-like covariance functions for smooth processes on a sphere (2015, methodology): “Nonetheless, as Gneiting (2013) argues, great circle distance is a physically more natural distance metric on the surface of a sphere, and it is worth developing valid covariance models with great circle distance.”
Local Gaussian Process Approximation for Large Computer Experiments (2013, methodology): “ 2012; Sang and Huang, 2012). Our contribution has aspects in common with all of these approaches and several others by association (e.g., Nychka et al., 2002; Quinonero{Candela~ and Rasmussen, 2005; Furrer et al., 2006). It is reminiscent of ad hoc methods based on local kriging neighborhoods (e.g.”
A full scale approximation of covariance functions for large spatial data sets (2012, methodology): “If the tapered part is void, we obtain the predictive process of Banerjee et al. (2008); if the set SÅ of locations is empty, then the predictive process part is void and we obtain the tapered version of the original covariance function as used in Furrer et al. (2006) and Kaufman et al. (2008).”
Fixed rank kriging for very large spatial data sets (2008, background): “One avenue of recent research has been to approximate the kriging equations (Nychka et al., 1996, 2002; Nychka, 2000; Billings et al., 2002 a, b; Furrer et al., 2006; Quiñonero-Candela and Rasmussen, 2005).”
Separable approximations of space‐time covariance matrices (2007, methodology): “Another interesting direction consists in combining separable approximations with the tapering approach of Furrer et al. (2006). Indeed, in the NKPST problem, the optimization of (6) can be performed under constraints in order for the solution to have a prescribed structure, such as sparsity pattern”
Likelihood approximation with hierarchical matrices for large spatial datasets (2017, background): “During the past two decades, a large amount of research has been devoted to tackling the aforementioned computational challenge of developing scalable methods: for example, covariance tapering [21, 36, 60], likelihood approximations in both the spatial [64] and spectral [19] domains, latent processe”
Dimension reduction and alleviation of confounding for spatial generalized linear mixed models (2010, background): “…extensive literature detailing many approaches, e.g. process convolution (Higdon, 2002), fixed rank kriging (Cressie and Johannesson, 2008), Gaussian predictive process models (Banerjee et al., 2008), covariance tapering (Furrer et al., 2006) and approximation by a GMRF (Rue and Tjelmeland, 2002).”
On fixed-domain asymptotics and covariance tapering in Gaussian random field models (2011, background): “MR0543837 [10] Kaufman, C. G., Schervish, M. J. and Nychka, D. W. (2008).”
Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants (2007, methodology): “The technique is also considered in the context of spatial prediction to introduce sparseness in the covariance structure (Furrer et al., 2006).”
Statistical Properties of Covariance Tapers (2013, methodology): “Another approach that may have broader scope is covariance tapering (Furrer, Genton, and Nychka 2006): suppose Kt is a covariance function that is 0 for all x and y sufficiently distant and define K̃ by K̃(x, y) = K(x, y)Kt (x, y), which is a valid covariance function since it is the product of…”
On the relationship between conditional (CAR) and simultaneous (SAR) autoregressive models (2017, methodology): “Other approaches 294 include tapering (Furrer et al., 2006) and thresholding (Bickel and Levina, 2008) for covariance 295 matrices (for a broad treatment, see Pourahmadi, 2013).”
Efficient Emulators for Multivariate Deterministic Functions (2008, background): “Additional sparsity can be imposed by tapering W r or W s (Furrer et al. 2006).”
Spatio-temporal modeling of particulate matter concentration through the SPDE approach (2012, neutral): “For facing the “big n problem” in the recent literature some solutions have been suggested such as, for example, covariance tapering, predictive process models and low rank kriging (see Banerjee et al 2008; Cressie and Johan nesson 2008; Furrer et al 2006).”
Classes of compactly supported covariance functions for multivariate random fields (2015, methodology): “This class of covariance functions has been used repeatedly in applications involving so-called tapered likelihoods (Furrer et al. 2006; Kaufman et al. 2008; Du et al. 2009).”
Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets (2014, background): “ low-rank models tend to perform better (Finley et al. 2009; Banerjee et al. 2010; Sang and Huang 2012), they increase the computational burden. Sparse methods include covariance tapering (see, e.g., Furrer et al. 2006; Kaufman et al. 2008; Du et al. 2009; Shaby and Ruppert 2012), which introduces s”