Modeling spatially dependent functional data via regression with differential regularization

open4siWe propose a method for modeling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of the phenomenon under study, formalized in terms of a time-dependent partial differential equation. The method is implemented using a discretization based on finite elements in space and finite differences in time. This non-tensor product basis allows to handle efficiently data distributed over complex domains and where the shape of the domain influences the phenomenon's behavior. Moreover, the method can comply with specific conditions at the boundary of the domain of interest. Simulation studies compare the proposed model to available techniques for spatio-temporal data. The method is also illustrated via an application to the study of blood-flow velocity field in a carotid artery affected by atherosclerosis, starting from echo-color doppler and magnetic resonance imaging data. (C) 2018 Elsevier Inc. All rights reserved.openArnone, Eleonora; Azzimonti, Laura; Nobile, Fabio; Sangalli, Laura M.Arnone, Eleonora; Azzimonti, Laura; Nobile, Fabio; Sangalli, Laura M

Modeling spatial anisotropy via regression with partial differential regularization

We consider the problem of analyzing spatially distributed data characterized by spatial anisotropy. Following a functional data analysis approach, we propose a method based on regression with partial differential regularization, where the differential operator in the regularizing term is anisotropic and is derived from data. We show that the method correctly identifies the direction and intensity of anisotropy and returns an accurate estimate of the spatial field. The method compares favorably to both isotropic and anisotropic kriging, as tested in simulation studies under various scenarios. The method is then applied to the analysis of Switzerland rainfall data