Prof. Dr. Laura Maria Sangalli, Laboratory for Modeling and Scientific Computing MOX (Politecnico di Milano, Italy), will give a talk on "Functional Data Analysis, Spatial Data Analysis and Partial Differential Equations: a fruitful union". It will take place on October, 19th 13:15 in G03-214. There will also be some coffee and tea afterwards in G02-215.
I will present a novel class of models for the analysis of spatially (or space-time) distributed data, based on the idea of regression with differential regularizations. The models merge statistical methodology and numerical analysis techniques. Thanks to the combination of potentialities from these different scientific areas, the proposed method has important advantages with respect to classical spatial data analysis techniques. Spatial Regression with differential regularizations is able to efficiently deal with data distributed over complex planar domains as well as over manifold domains. Moreover, it can comply with specific conditions at the boundaries of the problem domain, which is fundamental in many applications to obtain meaningful estimates. The proposed models can also incorporate problem-specific priori information about the spatial (or space-time) structure of the phenomenon under study, naturally accounting for anisotropy and non-stationarity. The use of advanced numerical analysis techniques, and in particular of the finite element method or of isogeometric analysis, makes the models computationally very efficient. I will illustrate the models via an application in the neurosciences. Based on joint work with John Aston, Laura Azzimonti, Mara Bernardi, Bree Ettinger, Michelle Carey, Eardi Lila, Fabio Nobile, Simona Perotto, Jim Ramsay, Piercesare Secchi.
Lecture Series: Oberseminar zur Stochastik