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

非常高维数据的分析对统计学家提出了一系列独特的挑战：设计可行的算法，估计和可视化以及推理。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，特别强调高通量基因组数据。这包括来自表达微阵列实验的数据，该实验可以在单个生物测定中询问多达50k个基因，基因型信息的全基因组扫描，例如Affytechnic GeneChip Human Mapping阵列，该阵列可以询问人类基因组上多达500k个标记（所谓的单核苷酸多态性，其是基因组上占绝大多数遗传差异的位置），并且根据蛋白质组学实验，例如串联质谱法，其目前用于在一个实验中检测数万或数十万种蛋白质的存在，并且正在研究定量使用。虽然每个数据示例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，可以通过一般统计研究来解决。这项研究计划的结果将有利于统计界，通过引入新的方法进行统计分析和高维数据的可视化，并通过激励在这一非常重要的领域进一步研究，以及生物学家和临床医生通过扩大统计方法和软件工具的工具箱，可以应用于他们的基因组实验。作为这项工作的一部分，我们将在真实的数据上应用和验证新方法，对重要的临床和生物学实验进行初步和次要分析。这项工作的长期目标是将高维数据的理论统计、计算机技术的巨大进步和由此产生的统计分析新方法以及生物研究中的高通量革命的一些结果联系起来，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.