|Abstract:|| We propose an innovative method for the accurate estimation of surfaces and spatial fields when a prior knowledge on the phenomenon under study is available. The prior knowledge included in the model derives from physics, physiology or mechanics of the problem at hand, and is formalized in terms of a partial differential equation governing the phenomenon behavior, as well as conditions that the phenomenon has to satisfy at the boundary of the problem domain. The proposed models exploit advanced scientific computing techniques and specifically make use of the Finite Element method. The estimators have a typical penalized regression form and the usual inferential tools are derived. Both the pointwise and the areal data frameworks are considered. The driving application concerns the estimation of the blood flow velocity field in a section of a carotid artery, using data provided by echo-color doppler; this applied problem arises within a research project that aims at studying atherosclerosis pathogenesis. Keywords: functional data analysis, spatial data analysis, object-oriented data analysis, penalized regression, Finite Elements.|
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Laura Azzimonti, Laura M. Sangalli, Piercesare Secchi, Maurizio Domanin, Fabio Nobile (2014),
Blood flow velocity field estimation via spatial regression with PDE penalization,
Journal of the American Statistical Association, Theory and Methods, DOI. 10.1080/01621459.2014.946036.