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    Efficiency Assessment of Approximated Spatial Predictions for Large Datasets

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    Type
    Preprint
    Authors
    Hong, Yiping cc
    Abdulah, Sameh
    Genton, Marc G. cc
    Sun, Ying cc
    KAUST Department
    Extreme Computing Research Center
    Statistics Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-11-11
    Permanent link to this record
    http://hdl.handle.net/10754/660757
    
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    Abstract
    Due to the well-known computational showstopper of the exact Maximum Likelihood Estimation (MLE) for large geospatial observations, a variety of approximation methods have been proposed in the literature, which usually require tuning certain inputs. For example, the Tile Low-Rank approximation (TLR) method, a recently developed efficient technique using parallel hardware architectures, involves many tuning inputs including the numerical accuracy, which needs to be selected according to the features of the true process. To properly choose the tuning inputs, it is crucial to adopt a meaningful criterion for the assessment of the prediction efficiency with different inputs. Unfortunately, the most commonly-used mean square prediction error (MSPE) criterion cannot directly assess the loss of efficiency when the spatial covariance model is approximated. In this paper, we present two other criteria, the Mean Loss of Efficiency (MLOE) and Mean Misspecification of the Mean Square Error (MMOM), and show numerically that, in comparison with the common MSPE criterion, the MLOE and MMOM criteria are more informative, and thus more adequate to assess the loss of the prediction efficiency by using the approximated or misspecified covariance models. Thus, our suggested criteria are more useful for the determination of tuning inputs for sophisticated approximation methods of spatial model fitting. To illustrate this, we investigate the trade-off between the execution time, estimation accuracy, and prediction efficiency for the TLR method with extensive simulation studies and suggest proper settings of the TLR tuning inputs. We then apply the TLR method to a large spatial dataset of soil moisture in the area of the Mississippi River basin, showing that with our suggested tuning inputs, the TLR method is more efficient in prediction than the popular Gaussian predictive process method.
    Sponsors
    This work is partially supported by the NSFC (No. 11931001).
    Publisher
    arXiv
    arXiv
    1911.04109
    Additional Links
    https://arxiv.org/pdf/1911.04109
    Collections
    Preprints; Extreme Computing Research Center; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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