Approximations of High-Order Spatial Statistics Through Decomposition

Goodfellow, Ryan; Mustapha, Hussein; Dimitrakopoulos, Roussos

doi:10.1007/978-94-007-4153-9_8

Cited by 2 publications

(2 citation statements)

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“…Higher-order spatial statistics were first introduced by Dimitrakopoulos et al (2010), followed by a number of studies including Mustapha and Dimitrakopoulos (2010a), Machuca-Mory and Dimitrakopoulos (2012, and Goodfellow et al (2012). In these studies, the particular form of the higher-order spatial statistics are spatial cumulants, which are used to evaluate the dependence structure of a spatially distributed random variable at an unsampled location x 0 , denoted Z(x 0 ), based on values at some sample locations in the neighbourhood.…”

Section: Introductionmentioning

confidence: 99%

“…Such ineffectiveness is especially severe in geological or environmental studies, as discussed by , Strebelle (2002) and Tjelmeland and Besag (1998). In the past decade, various techniques have been developed to improve the reliability of characterizing random fields, such as bootstrapping (Kleijnen et al, 2012;Schelin and Luna, 2010;Stein, 2008, 2004;Mukul et al, 2004), copula-based methods (Kazianka, 2013;Pilz et al, 2012;Kazianka andPilz, 2010a, 2010b;Bárdossy and Li, 2008;Bárdossy, 2006), kernel-based methods (Honarkhah and Caers, 2010;Scheidt and Caers, 2010, 2009a, 2009b), Bayesian (Nieto-Barajas and Sinha, 2014Troldborg et al, 2012;Pilz et al, 2012;Kazianka andPilz, 2011, 2012), multi-point simulation methods (De Iaco, 2013;Boucher, 2009;Chugunova and Hu, 2008;Wu et al, 2008;Mirowski et al, 2008;Arpat and Caers, 2007;Zhang et al, 2006;Strebelle, 2002), multi-scale simulations using wavelets (Chatterjee and Dimitrakopoulos, 2012;Dimitrakopoulos, 2009, 2008), and spatial-cumulant-based simulation methods (Goodfellow et al, 2012;MachucaMory and Dimitrakopoulos, 2012;, Dimitrakopoulos et al, 2010.…”

Section: Introductionmentioning

confidence: 99%

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A new approach to spatial data interpolation using higher-order statistics

Liu

Anh

McGree

et al. 2014

Stoch Environ Res Risk Assess

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Abstract:Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first-and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting nonGaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility.Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function (CPDF) is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

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Section: Introductionmentioning

confidence: 99%