Estimating deformations of isotropic Gaussian random fields on the plane

By Ethan B. Anderes, Michael L. Stein. 2008

94 citations recorded by the source corpus.

This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on R 2 based on dense observations of a single realization of the deformed random field. Under this framework we investigate the identification and estimation of deformations. We then present a complete methodological package-from model assumptions to algorithmic recovery of the deformation-for the class of nonstationary processes obtained by deforming isotropic Gaussian random fields.

Subfields: Applied Mathematics, Environmental Engineering, Statistics and Probability

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In Environmental Engineering

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Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “There are many other examples of non-stationary covariance functions [70], [121], [132], [126], [118], [22], [3], [54] that have been proposed for GP regression along with closely related output warping techniques [141] that can also model certain kinds of non-stationary processes. b) Partitioning:…”
Non-Stationary Dependence Structures for Spatial Extremes (2014, background): “Alternatively, Sampson and Guttorp (1992), Perrin and Monestiez (1999), Schmidt and O’Hagan (2003) and Anderes and Stein (2008) created nonstationary processes by smooth deformations of isotropic random fields.”
Moving window kriging with geographically weighted variograms (2010, background): “Computationally, MWK–GWV is slightly more demanding than MWK–CV; and both models are affected by large datasets (a problem routinely encountered with numerous spatial methods, see Banerjee et al. 2008, for recent advances). Additional work could consider the effects of sample configuration on MWK pe”
Second-order non-stationary modeling approaches for univariate geostatistical data (2017, methodology): “Anderes and Stein (2011) propose a weighted local likelihood approach for estimating parameters of closedform non-stationary covariance functions with locally varying geometric anisotropy. Fouedjio et al. (2016) propose a free distribution approach involving a local stationary variogram kernel estim”
On the consistent separation of scale and variance for Gaussian random fields (2009, background): “as n→∞ (for details see [3], Lemma 3, page 41).”
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)].”
Nonstationary covariance models for global data (2008, methodology): “example, in Sampson and Guttorp (1992), Perrin and Senoussi (2000), Schmidt and O’Hagan (2003), Clerc and Mallat (2003) and Anderes and Stein (2008). Kernel convolution and its variants have been applied in several papers to create nonstationary covariance functions such as in Higdon (1998), Higdon,”