Title: Kriging for Hilbert data over complex domains through random domain decomposition
Authors: Alessandra Menafoglio - Politecnico di Milano (Italy) [presenting]
Piercesare Secchi - Politecnico di Milano (Italy)
Giorgia Gaetani - Politecnico di Milano (Italy)
Abstract: The analysis of complex data distributed over large or highly textured regions poses new challenges for spatial statistics. Indeed, methods to deal with spatial data often rely upon global models for the dependence of the field, and are thus hardly usable in the presence of textured or convoluted domains, with holes or barriers. We propose a novel methodology for the spatial prediction of Hilbert data distributed in such kinds of domains, which cope with the data and domain complexities through a divide-et-impera approach. As a key element of innovation, we propose to perform repeated Random Domain Decompositions (RDDs), each defining a set of homogeneous sub-regions where to perform locally stationary analyses. We account for the complexity of the domain by defining these partitions through appropriate non-Euclidean metrics, that properly represent the adjacency relationships among the observations over the domain. As an insightful illustration of the potential of the methodology, we consider the spatial prediction of density data in non-convex and irregularly shaped estuarine system.