Statistics for high-dimensional data with applications in analysis of high-throughput genomics experiments

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The analysis of very high-dimensional data poses a unique set of challenges for statisticians: in designing feasible algorithms, in estimation and visualization, and in inference. In this research project I propose to continue my work in addressing some issues in all these areas, with a special emphasis on high-throughput genomic data. This includes data from expression microarray experiments, which can interrogate up to 50k genes in a single biological assay, genome-wide scans of genotypic information, such as Affymetrix GeneChip Human Mapping arrays which can interrogate up to 500k markers on a human genome (so-call Single Nucleotide Polymorphism which are locations on a genome accounting for vast majority of genetic differences), and from proteomics experiments, such as Tandem Mass Spectrometry that is being currently used to detect presence of tens or hundreds of thousands of proteins in one experiment, and is being researched for quantitative use. While the nature of each of these data examples can be very different, as well as the potential applications of such technologies (which are now widely used for both basic and clinical research), they all share a number of characteristics, that can be addressed by general statistical research. The results of this research program will benefit both the statistical community, by introducing new methods for statistical analysis and visualization of high-dimensional data and by motivating further research in this very important area, as well as biologists and clinicians by expanding the toolbox of statistical methods and software tools that can be applied to their genomic experiments. As part of this work we  will apply and validate the new methods on real data to perform  primary and secondary analysis of important clinical and biological experiments. The long term objective of this work is to connect the some results in theoretical statistics of high-dimensional data, great advances computer technology and the resulting novel approaches to statistical analysis, and the high-throughput revolution in biological research to help answer important questions in biological and  health sciences.