Collaborative Research: Analysis of Functional and High-Dimensional Data with Applications

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This project deals with statistical inference inphenomena that result in massive, multidimensional and/orfunctional data sets. Prime examples are geophysical, biomedical,and internet related data. In addition to high dimensionality, suchdata are often characterized by self-affinity and requirenon-standard (functional) models for their modeling and subsequentstatistical analysis. The methodology to be developed will advanceboth the theory and practice of functional data analysis, a veryfast-developing and modern area of statistics. The common and novelfeatures of the statistical methods proposed here lie in the natureof analyzed data. The data sets are massive, multidimensional,functional, and possibly self-affine (fractal or multifractal).Recent progress in multiscale data representations provide naturaland efficient environments for (i) developing scale-sensitiveanalyzing tools for estimation, testing, classification, anddeconvolution, and (ii) describing, summarizing, and modelingself-similar data. Bayesian methodology will be used wheneveravailable prior information can be incorporated or whenever sensibleautomatic priors are possible.Development of new inferential methodologies is critical for thestatistical support of recent scientific initiatives and newlyemerging technologies. The proposed research is application driven,so the specificities of the application fields influence the designand focus of the methodology. Techniques suggested in the proposaldeal with problems of testing of efficiency of new medicaltreatments, target detection and classification as well asclassification of medical images, or more accurate recovery of radaror satellite data. Hence, the methodologies which result from theproposal are applicable in such areas of strategic interest ashealth and medicine and homeland security. In addition tomethodological impact, the proposed research has a strongeducational component consisting of training graduate students,involving undergraduate students in research projects, conductinginter-departmental seminars, increasing awareness of mathematicseducation among the work force, and attracting minority and femalestudents.