Use of a tree‐structured hierarchical model for estimation of location and uncertainty in multivariate spatial data

Analysis and modeling of spatial data are of considerable interest in many applications. However, the prediction of geographical features from a set of chemical measurements on a set of geographically distinct samples has never been explored. We report a new, tree‐structured hierarchical model for the estimation of geographical location of spatially distributed samples from their chemical measurements. The tree‐structured hierarchical modeling used in this study involves a set of geographic regions stored in a hierarchical tree structure, with each nonterminal node representing a classifier and each terminal node representing a regression model. Once the tree‐structured model is constructed, given a sample with only chemical measurements available, the predicted regional location of the sample is gradually restricted as it is passed through a series of classification steps. The geographic location of the sample can be predicted using a regression model within the terminal subregion. We show that the tree‐structured modeling approach provides reasonable estimates of geographical region and geographic location for surface water samples taken across the entire USA. Further, the location uncertainty, an estimate of a probability that a test sample could be located within a pre‐estimated, joint prediction interval that is much smaller than the terminal subregion, can also be assessed. Copyright © 2014 John Wiley & Sons, Ltd.

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