Collaborative proposal: Variable Selection in the high dimensional, low sample size setting -- Beyond the Linear Regression and Normal Errors Model

革命性的新技术正在产生高通量的生物数据，其分辨率在十年前是不可想象的。这些新形式的数据给统计学家和计算机科学家带来了巨大的挑战和机遇。该项目开发了新的复杂的统计方法和计算算法来分析和整合复杂的高维数据。这项工作的动机是与康奈尔大学伊萨卡分校和威尔康奈尔医学院的领先生物科学家合作，他们在不同的研究领域工作，包括植物生物学、营养学、神经学、癌症表观基因组学和兽医学。该项目的目标是为高维、低样本量、高通量的生物数据开发新的统计模型和计算算法，包括微阵列分析、定量性状位点鉴定、关联制图、无标签鸟枪蛋白质组学和代谢组学的新方法。所提出的方法涉及现代统计构建模块的创新扩展，包括使用随机效应进行正则化，收缩估计，贝叶斯统计以及用于后验分类和预测的混合。提出了期望最大化算法的新改进，以实现可扩展和高效的模型拟合和推理。

Revolutionary new technologies are producing high-throughput biological data at a resolution that was unthinkable only a decade ago. These new forms of data pose enormous challenges and opportunities for statisticians and computer scientists. This project develops new sophisticated statistical methods and computational algorithms for analyzing and integrating complex high-dimensional data. The work is motivated by collaborations with leading biological scientists at Cornell-Ithaca and Weill Cornell Medical College working in diverse research areas including plant biology, nutrition, neurology, cancer epigenomics, and veterinary medicine. The goal of this project is to develop new statistical models and computational algorithms for high-dimensional, low sample size, high-throughput biological data, including new methods for the analysis of microarrays, the identification of quantitative trait loci, association mapping, label-free shotgun proteomics and metabolomics. The proposed methods involve innovative extensions of modern statistical building blocks, including the use of random effects for regularization, shrinkage estimation, Bayesian statistics, and mixtures for posterior classification and prediction. Novel modifications of the expectation-maximization algorithm are proposed for scalable and efficient model fitting and inference.