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Abstract:
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In spatial statistics, the kriging predictor is the best linear predictor at unsampled locations for Gaussian processes. However, many real-world processes are non-Gaussian. In this paper, we formulate the spatial probabilistic prediction problem for non-Gaussian random fields. We create sets of binary observations by thresholding the random field at different quantile levels, and then we treat them as multivariate binary spatial fields and apply cokriging for spatial interpolation. In many geostatistical methods, the dependence structure is described using the variograms, which are sensitive to outliers and strongly influenced by the marginal distribution of the random field. In this paper, we use copulas to model the dependence structure without any assumptions on marginal distributions. The predictive performance of multilevel indicator kriging has been demonstrated using simulation studies and proposed copula-based methods perform better than the variogram approach and Gaussian kriging. We illustrate our methods on the dataset of precipitation in Spain during November 2019 and obtain probability exceedance maps for high precipitation intensities.
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