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Stochastic Local Interaction Model: An Alternative to Kriging for Massive Datasets

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Abstract

Classical 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).

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Acknowledgements

The authors would like to thank Ricardo Olea (United States Geological Survey, Reston, Virginia, USA) who provided the coal data analyzed and graciously read a draft of this manuscript, offering valuable comments and insights.

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Authors and Affiliations

  1. School of Mineral Resources Engineering, Technical University of Crete, Chania, 73100, Greece

    Dionissios T. Hristopulos

  2. School of Mineral Resources Engineering, Technical University of Crete, Chania, 73100, Greece

    Andrew Pavlides, Vasiliki D. Agou & Panagiota Gkafa

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  1. Dionissios T. Hristopulos
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  2. Andrew Pavlides
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  3. Vasiliki D. Agou
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  4. Panagiota Gkafa
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Correspondence to Dionissios T. Hristopulos.

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Hristopulos, D.T., Pavlides, A., Agou, V.D. et al. Stochastic Local Interaction Model: An Alternative to Kriging for Massive Datasets. Math Geosci 53, 1907–1949 (2021). https://doi.org/10.1007/s11004-021-09957-7

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