Random domain decompositions for object-oriented Kriging over complex domains

We propose a new methodology for the analysis of spatial fields of object data distributed over complex domains. Our approach enables to jointly handle both data and domain complexities, through a divide et impera approach. As a key element of innovation, we propose to use a random domain decomposition, whose realizations define sets of homogeneous sub-regions where to perform simple, independent, weak local analyses (divide), eventually aggregated into a final strong one (impera). In this broad framework, the complexity of the domain (e.g., strong concavities, holes or barriers) can be accounted for by defining its partitions on the basis of a suitable metric, which allows to properly represent the adjacency relationships among the complex data (such as scalar, functional or constrained data) over the domain. As an illustration of the potential of the methodology, we consider the analysis and spatial prediction (Kriging) of the probability density function of dissolved oxygen in the Chesapeake Bay.