A novel approach to the analysis of spatial and functional data over complex domains

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 work in particular focuses on data displaying complex spatial dependencies, where the complexity can for instance be due to the complex physics of the problem or the non-trivial conformation of the domain where the data are observed.