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Stochastic local interaction model: an alternative to kriging for massive datasets

Christopoulos Dionysios, Pavlidis Andreas, Agou Vasiliki, Gafa Panagiota

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Extent43 pagesen
TitleStochastic local interaction model: an alternative to kriging for massive datasetsen
CreatorChristopoulos Dionysiosen
CreatorΧριστοπουλος Διονυσιοςel
CreatorPavlidis Andreasen
CreatorΠαυλιδης Ανδρεαςel
CreatorAgou Vasilikien
CreatorΑγου Βασιλικηel
CreatorGafa Panagiotaen
CreatorΓκαφα Παναγιωταel
Content SummaryClassical geostatistical methods face serious computational challenges if they are confronted with large spatial datasets. The stochastic local interaction (SLI) approach does not require matrix inversion for parameter estimation, spatial prediction, and uncertainty estimation. This leads to better scaling of computational complexity and storage requirements with data size than standard (i.e., without size-reducing modifications) kriging. This contribution presents a simplified SLI model that can handle large data. The SLI method constructs a spatial interaction matrix (precision matrix) that adjusts with minimal user input to the data values, their locations, and sampling density variations. The precision matrix involves compact kernel functions which permit the use of sparse matrix methods. It is proved that the precision matrix of the proposed SLI model is strictly positive definite. In addition, parameter estimation based on likelihood maximization is formulated, and computationally relevant properties of the likelihood function are studied. The interpolation performance of the SLI method is investigated and compared with ordinary kriging using (i) synthetic non-Gaussian data and (ii) coal thickness measurements from approximately 11,500 drill holes (Campbell County, Wyoming, USA).en
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Date of Item2022-11-04-
Date of Publication2021-
SubjectFast interpolationen
SubjectBig dataen
SubjectKernel functionen
SubjectStatistical learningen
SubjectGaussian Markov random fieldsen
SubjectNatural resources estimationen
Bibliographic CitationD. T. Hristopulos, A. Pavlides, V. D. Agou, and P. Gkafa, “Stochastic local interaction model: an alternative to kriging for massive datasets,” Math. Geosci., vol. 53, no. 8, pp. 1907–1949, Nov. 2021, doi: 10.1007/s11004-021-09957-7.en