Envelope Models and Methods for Efficient Multivariate Analysis with Applications to Tissue Engineering

用于高效多元分析的包络模型和方法及其在组织工程中的应用

• 批准号: 1007547
• 负责人: Ralph Cook
• 金额: $ 30.99万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-15 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007547&HistoricalAwards=false
• 关键词: Envelope; Models; Methods; Efficient; Multivariate

The investigator and his colleagues propose to develop a new class of statistical tools -- called envelopes -- for studying multivariate data. Enveloping is based on novel parameterizations that use reducing subspaces to link a location matrix L with a dispersion matrix D. For instance, the outer envelope is the smallest reducing subspace of D that contains the span of L, while the inner envelope is the largest reducing subspace of D that is contained within the span of L. In multivariate linear regression, the maximum likelihood estimator of the coefficient matrix L based on an envelope model can be substantially less variable than the maximum likelihood estimator under the classical normal model, particularly when the mean function varies in directions that are orthogonal to the directions of maximum variation for the dispersion matrix. It is expected that similar results will hold in other multivariate areas, like discriminant analysis and functional data analysis. Enveloping is a new paradigm for addressing multivariate statistical problems that has the potential to facilitate interpretation, to improve analyses that might otherwise be tenuous and to produce truly massive gains in efficiency relative to standard methods.Technological advances in many scientific fields have been followed by configurations of multivariate data that strain or are beyond the capabilities of standard statistical theory and methods. More than ever before, understanding experimental evidence and exploring scientific hypotheses require methods to meaningfully study contemporary data. This is particularly true in the life sciences, where the ability to extract the relevant information from a complex body of data is paramount. The investigator and his colleagues plan to study a new class of multivariate statistical methods that are capable of efficiently extracting relevant information for a given purpose from complex data. For instance, the overarching goal in tissue engineering is to gain the ability to replace damaged human connective tissue with viable tissue patches fabricated in vitro. Current technology has failed to reach this goal because tissues grown in vitro lack adequate mechanical integrity for in vivo applications. The mechanical integrity of tissues is controlled by a network of several hundred intercellular signaling proteins that shape long-term tissue growth and can be measured by mass spectrometry. The statistical objective here is to identify the most important stimuli and to extract the relevant information by reducing the signaling proteins to a few key protein indices that can be monitored during in vitro growth and directed by the external stimuli.

研究人员和他的同事们建议开发一类新的统计工具-称为信封-用于研究多变量数据。 包络是基于新的参数化，使用减少子空间链接的位置矩阵L与色散矩阵D。例如，外包络是包含L的跨度的D的最小约简子空间，而内包络是包含在L的跨度内的D的最大约简子空间。 在多元线性回归中，基于包络模型的系数矩阵L的最大似然估计量的可变性可以比经典正态模型下的最大似然估计量小得多，特别是当均值函数在与分散矩阵的最大变化方向正交的方向上变化时。 预计类似的结果将在其他多变量领域，如判别分析和函数数据分析。 包络分析是一种新的处理多元统计问题的方法，它有可能促进解释，改善原本可能是脆弱的分析，并产生相对于标准方法的真正巨大的效率增益。许多科学领域的技术进步之后，多元数据的配置应变或超出了标准统计理论和方法的能力。理解实验证据和探索科学假设比以往任何时候都更需要有意义地研究当代数据的方法。在生命科学中尤其如此，从复杂的数据中提取相关信息的能力至关重要。 研究人员和他的同事们计划研究一类新的多元统计方法，这些方法能够从复杂的数据中有效地提取用于给定目的的相关信息。 例如，组织工程的首要目标是获得用体外制造的活组织补片替换受损的人类结缔组织的能力。目前的技术未能达到这一目标，因为在体外生长的组织缺乏足够的机械完整性，在体内应用。组织的机械完整性由数百种细胞间信号蛋白组成的网络控制，这些蛋白形成长期的组织生长，并且可以通过质谱法进行测量。 这里的统计目标是识别最重要的刺激，并通过将信号蛋白减少到几个关键蛋白质指数来提取相关信息，这些指数可以在体外生长过程中进行监测并由外部刺激指导。