This project deals with statistical inference in phenomena that result in massive, multidimensional and/or functional data sets. Prime examples are geophysical, biomedical, and internet related data. In addition to high dimensionality, such data are often characterized by self-affinity and require non-standard (functional) models for their modeling and subsequent statistical analysis. The methodology to be developed will advance both the theory and practice of functional data analysis, a very fast-developing and modern area of statistics. The common and novel features of the statistical methods proposed here lie in the nature of analyzed data. The data sets are massive, multidimensional, functional, and possibly self-affine (fractal or multifractal). Recent progress in multiscale data representations provide natural and efficient environments for (i) developing scale-sensitive analyzing tools for estimation, testing, classification, and deconvolution, and (ii) describing, summarizing, and modeling self-similar data. Bayesian methodology will be used whenever available prior information can be incorporated or whenever sensible automatic priors are possible.
Development of new inferential methodologies is critical for the statistical support of recent scientific initiatives and newly emerging technologies. The proposed research is application driven, so the specificities of the application fields influence the design and focus of the methodology. Techniques suggested in the proposal deal with problems of testing of efficiency of new medical treatments, target detection and classification as well as classification of medical images, or more accurate recovery of radar or satellite data. Hence, the methodologies which result from the proposal are applicable in such areas of strategic interest as health and medicine and homeland security. In addition to methodological impact, the proposed research has a strong educational component consisting of training graduate students, involving undergraduate students in research projects, conducting inter-departmental seminars, increasing awareness of mathematics education among the work force, and attracting minority and female students.
