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There are various occasions where simple,ordinary,and universal kriging techniques may find themselves incapa-ble of performing spatial prediction directly or efficiently.One type of application concerns quantification of cumulative distri-bution function (CDF) or probability of occurrences of categorical variables over space.The other is related to optimal use of co-variation inherent to multiple regionalized variables as well as spatial correlation in spatial prediction.This paper extends geostatistics from the realm of kriging with uni-variate and continuous regionalized variables to the territory of indicator and multivariate kriging,where it is of ultimate importance to perform non-parametric estimation of probability distributions and spatial prediction based on co-regionalization and multiple data sources,respectively.