Functional and complex data – new methods merging statistics, scientific computing and engineering

Recent years have seen an explosive growth in the recording of increasingly complex and high-dimensional data. Classical statistical methods are often unfit to handle such data, whose analysis calls for the definition of new methods merging ideas and approaches from statistics, applied mathematics and engineering. This seminar in particular focuses on functional and spatial data defined over complex multidimensional domains, including curved bi-dimensional domains and non-convex three-dimensional domains. I will present an innovative class of methods, based on regularizing terms involving partial differential equations. The proposed methods make use of advanced numerical techniques, such as finite element analysis and isogeometric analysis. An illustration to the analysis of neuroimaging data is provided. In this applicative domain, the proposed methods offer important advantages with respect to the best state of art techniques, allowing to correctly take into account to complex anatomy of the brain.

Record link: https://videos.univ-grenoble-alpes.fr/video/19727-seminaire-ljk-21-05-20-laura-maria-sangalli/