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

Liu, Shen, Anh, Vo, McGree, James, Kozan, Erhan, & Wolff, Rodney C. (2015) A new approach to spatial data interpolation using higher-order statistics. Stochastic Environmental Research and Risk Assessment, 29(6), pp. 1679-1690.

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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 non-Gaussian 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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1 citations in Scopus
1 citations in Web of Science®
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ID Code: 78926
Item Type: Journal Article
Refereed: Yes
Keywords: Geostatistics, Interpolation, Uncertainty quantification, Mineral deposit
DOI: 10.1007/s00477-014-0985-1
ISSN: 1436-3259
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Applied Statistics (010401)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100) > Pattern Recognition and Data Mining (080109)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > RESOURCES ENGINEERING AND EXTRACTIVE METALLURGY (091400) > Mining Engineering (091405)
Australian and New Zealand Standard Research Classification > ECONOMICS (140000) > APPLIED ECONOMICS (140200) > Environment and Resource Economics (140205)
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 25 Nov 2014 23:52
Last Modified: 26 Jun 2017 04:27

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