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Abstract:
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Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. We propose Spatial Meta Kriging (SMK) model to facilitate analysis of large point referenced datasets. SMK partitions large data into smaller subsets, fits hierarchical Bayesian spatial process regression model for each of these subsets independently and finally combines parametric and predictive inferences obtained from independent spatial regression models on subsets. The resulting procedure eliminates the need to store the entire data in one processor and offers an embarrassingly parallelizable inferential technique that assumes linear computation complexity in the number of spatial locations, thereby delivering substantial scalability. We demonstrate SMK with Gaussian process, covariance tapered Gaussian process and low-rank modified predictive process models to understand the performance of the proposed technique with various spatial regression models. We illustrate the computational and inferential benefits of the SMK using simulation experiments and also large scale MODIS atmospheric data for climate change.
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