Stochastic local interaction model: an alternative to kriging for massive datasetsStochastic local interaction model: an alternative to kriging for massive datasets Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2022-11-042021enClassical 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).http://creativecommons.org/licenses/by/4.0/Mathematical Geosciences5381907–1949 Christopoulos Dionysios Χριστοπουλος Διονυσιος Pavlidis Andreas Παυλιδης Ανδρεας Agou Vasiliki Αγου Βασιλικη Gafa Panagiota Γκαφα Παναγιωτα Springer Fast interpolation Big data Kernel function Statistical learning Gaussian Markov random fields Natural resources estimation