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.

View at publisher

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 (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.

Impact and interest:

1 citations in Scopus
Search Google Scholar™
1 citations in Web of Science®

Citation counts are sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

11 since deposited on 25 Nov 2014
9 in the past twelve months

Full-text downloads displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

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 > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 25 Nov 2014 23:52
Last Modified: 09 Aug 2016 07:29

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page