Research is proposed in the areas of medical image analysis and the gene expression micro-array analysis. These seemingly divergent fields have a common structure. The over-arching abstraction that contains them both is "High Dimension - Low Sample Size" (HDLSS). HDLSS data are completely outside of the domain of classical statistical multivariate analysis, because the critical first step of "sphering the data" can no longer be performed. This motivates the development of a very large new toolbox of statistical methods, which will be useful in fields far beyond those motivating this research. An important part of the proposed analytical work is the development of a completely new type of asymptotic analysis, where the sample size is fixed, and the dimension tends to infinity.
The proposed research will be on the development and assessment of new data analytical methods. These will provide critical statistical infrastructure for the large teams of people that are tackling current major challenges in the field of medicine. The first challenge is the ongoing war on cancer. The second challenge is to make the rapidly developing breakthroughs in medical imaging technology much more useful to practicing medical professionals. Both areas will be substantially benefited by the creative new methods of statistical analysis that will be developed during the course of this research.
