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

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, prediction, and uncertainty estimation. This leads to better scaling of complexity storage requirements data size than standard (i.e., without size-reducing modifications) kriging. contribution presents a simplified SLI model that can handle data. method constructs (precision matrix) adjusts minimal user input the values, their locations, sampling density variations. precision involves compact kernel functions which permit use sparse methods. It is proved proposed strictly positive definite. In addition, estimation based on likelihood maximization formulated, computationally relevant properties function studied. interpolation performance investigated compared ordinary kriging using (i) synthetic non-Gaussian (ii) coal thickness measurements from approximately 11,500 drill holes (Campbell County, Wyoming, USA).