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

Liu. Shen, Anh. Vo, McGree, James, Kozan, Erhan and Wolff, Rodney C. (2014) A new approach to spatial data interpolation using higher-order statistics. Stochastic Environmental Research and Risk Assessment, 29 6: 1679-1690. doi:10.1007/s00477-014-0985-1

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Author Liu. Shen
Anh. Vo
McGree, James
Kozan, Erhan
Wolff, Rodney C.
Title A new approach to spatial data interpolation using higher-order statistics
Journal name Stochastic Environmental Research and Risk Assessment   Check publisher's open access policy
ISSN 1436-3240
Publication date 2014-11-20
Year available 2014
Sub-type Article (original research)
DOI 10.1007/s00477-014-0985-1
Open Access Status File (Author Post-print)
Volume 29
Issue 6
Start page 1679
End page 1690
Total pages 12
Place of publication Heidelberg, Germany
Publisher Springer
Collection year 2015
Language eng
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 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 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.
Keyword Geostatistics
Uncertainty quantification
Mineral Deposits
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online ahead of print 20 November 2014.

Document type: Journal Article
Sub-type: Article (original research)
Collections: W.H. Bryan Mining Geology Research Centre
Official 2015 Collection
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Citation counts: TR Web of Science Citation Count  Cited 1 times in Thomson Reuters Web of Science Article | Citations
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Created: Fri, 28 Nov 2014, 09:04:13 EST by Rodney Wolff on behalf of WH Bryan Mining and Geology Centre