Indicator and multivariate geostatistics for spatial prediction

Abstract

There are various occasions where simple, ordinary, and universal kriging techniques may find themselves incapable of performing spatial prediction directly or efficiently. One type of application concerns quantification of cumulative distribution 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.