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

对高维数据的分析对统计学家提出了一系列独特的挑战：在设计可行的算法、估计和可视化以及推理方面。在这个研究项目中，我建议继续我的工作，解决所有这些领域的一些问题，特别是高通量基因组数据。这包括来自表达微阵列实验的数据，它可以在一次生物分析中询问多达50k个基因，全基因组的基因类型信息扫描，例如可以询问人类基因组上多达500k个标记的Affymetrix基因芯片人类图谱阵列(所谓的单核苷酸多态，它是基因组上解释绝大多数遗传差异的位置)，以及来自蛋白质组学实验的数据，例如目前正在用于检测一次实验中是否存在数万或数十万种蛋白质的串联质谱学，并正在研究用于定量用途。虽然每个数据例子的性质可能非常不同，以及这些技术的潜在应用(现在广泛用于基础和临床研究)，但它们都有一些共同的特征，可以通过一般的统计研究来解决。这一研究计划的结果将通过引入高维数据的统计分析和可视化的新方法，并通过激励这一非常重要的领域的进一步研究，以及通过扩展可应用于他们的基因组实验的统计方法和软件工具的工具箱，使生物学家和临床医生受益。作为这项工作的一部分，我们将在真实数据上应用和验证新方法，以对重要的临床和生物实验进行一次和二次分析。这项工作的长期目标是将高维数据理论统计的一些结果、计算机技术的巨大进步和由此产生的统计分析的新方法，以及生物学研究的高通量革命联系起来，以帮助回答生物和健康科学中的重要问题。

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.