Efficiency assessment of approximated spatial predictions for large datasets

Due to the well-known computational showstopper of exact Maximum Likelihood Estimation (MLE) for large geospatial observations, a variety approximation methods have been proposed in literature, which usually require tuning certain inputs. For example, recently developed Tile Low-Rank (TLR) method involves many parameters, including numerical accuracy. To properly choose it is crucial adopt meaningful criterion assessment prediction efficiency with different inputs, most commonly-used Mean Square Prediction Error (MSPE) and Kullback-Leibler Divergence cannot fully describe. In this paper, we present three other criteria, Loss Efficiency (MLOE), Misspecification (MMOM), Root mean square MOM (RMOM), show numerically that, comparison common MSPE criterion, our criteria are more informative, thus adequate assess loss by using approximated or misspecified covariance models. Hence, suggested useful determination parameters sophisticated spatial model fitting. illustrate this, investigate trade-off between execution time, estimation accuracy, TLR extensive simulation studies suggest proper settings parameters. We then apply dataset soil moisture area Mississippi River basin, compare Gaussian predictive process composite likelihood method, showing that can successfully be used keep accuracy applications.