Nonparametric Estimation of Nonstationary Spatial Covariance Structure

By P. Sampson, Peter Guttorp. 1992

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Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, methodology): “One strategy is to convert a stationary kernel into a nonstationary one by transforming x using a parametric warping function xðwÞ 1⁄4 wðxÞ and then applying a stationary kernel to xðwÞ [129], [145].”
On the Use of Non-Euclidean Distance Measures in Geostatistics (2007, background): “Sampson and Guttorp (1992) propose a similar approach to a different problem.”
Estimating deformations of isotropic Gaussian random fields on the plane (2008, background): “ngle realization of a deformed isotropic Gaussian random ﬁeld. The use of deformations to model nonstationary processes was ﬁrst introduced to the spatial statistics literature by Sampson and Guttorp [18]. Their work, as well as that of subsequent authors (see, e.g., [7, 11, 16, 19]) deals mostly wi”
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (2009, unknown): “Rue and Martino (2007) showed that the approximate posterior marginals for θwere accurate, whereas the error in the Gaussian approximation (4) was higher.”
Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets (2008, background): “One possible approach to this problem would be to consider the class of random ﬁelds that are stationary and isotropic subject to some transformation of the underlying space on which the process is deﬁned, as done by Sampson and Guttorp (1992).”
Some new random field tools for spatial analysis (2008, background): “(See, however, [13], which shows that if one is prepared to pay the price of moving to a higher dimensional scenario than the one inherent to the problem, there is a way around this.”
Kriging in the Presence of Locally Varying Anisotropy Using Non-Euclidean Distances (2009, methodology): “Further, MDS removes all anisotropy from the data ( Sampson and Guttorp 1992 )s o that a single isotropic variogram in q dimensions can reproduce the locally varying anisotropies as captured by the inter-point distance matrix (D).”
Considering covariates in the covariance structure of spatial processes (2011, background): “Notice that the inclusion of more axes gives the freedom to adjust better the observed correlations, as a correlation function inRT 1 fits the observed correlations perfectly (Sampson and Guttorp, 1992).”
Forward and Inverse Transformations between Cartesian and Channel-fitted Coordinate Systems for Meandering Rivers (2007, unknown): “by Smith and McLean (1984) has been widely used to model flow and sediment transport in meandering rivers (e.”
Estimation of a non-stationary model for annual precipitation in southern Norway using replicates of the spatial field (2014, methodology): “Deformation methods obtain a non-stationary model by deformation of a latent space where the process is stationary (Sampson and Guttorp, 1992), and the axes of this latent space can be defined by explanatory variables (Schmidt et al., 2011).”
Gaussian process product models for nonparametric nonstationarity (2008, methodology): “One of the .rst techniques was that of Sampson and Guttorp (1992), who model a spline-based mapping to a latent input space in which the data are stationary.”
Non-Stationary Dependence Structures for Spatial Extremes (2014, background): “ and Stein (2007, 2008), Castruccio and Stein (2013) and Castruccio and Genton (2014) advocated a spectral approach that provides exible non-stationary covariance models on the sphere. Alternatively, Sampson and Guttorp (1992), Perrin and Monestiez (1999), Schmidt and O’Hagan (2003) and Anderes and ”
Nonstationary spatial covariance functions (2005, background): “Another approach to producing explicit covariance functions with locally varying geometric anisotropies is to use spatial deformations (Sampson and Guttorp 1992, Perrin and Senoussi 2000, Sampson, Damian and Guttorp 2001, Schmidt and O’Hagan 2003, Clerc and Mallat 2003).”
Modeling Nonstationary Processes Through Dimension Expansion (2010, methodology): “First, the solar radiation dataset originally used in Sampson and Guttorp (1992) and used as a test-bed in various more recent image warping papers is studied.”
Interpolation of nonstationary air pollution processes: a spatial spectral approach (2002, methodology): “This approach is promising, and a quite different idea from earlier approaches for nonstationarity; see, for example, Sampson and Guttorp (1992), Guttorp and Sampson (1994), Haas (1995), and Nychka et al. (1999).”
Composite Gaussian process models for emulating expensive functions (2012, background): “…the literature focus on deriving complex nonstationary covariance functions such as by spatial deformations or kernel convolution approaches [e.g., see Sampson and Guttorp (1992), Higdon, Swall and Kern (1999), Schmidt and O’Hagan (2003), Paciorek and Schervish (2006) and Anderes and Stein (2008)].”