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

研究者和他的同事们提议开发一种新的统计工具——称为信封——用于研究多变量数据。包络是基于一种新颖的参数化，它使用约简子空间将位置矩阵L与色散矩阵D联系起来。例如，外层包络是包含L张成空间的D的最小约简子空间，而内层包络是包含在L张成空间内的D的最大约简子空间。基于包络模型的系数矩阵L的最大似然估计量可以比经典正态模型下的最大似然估计量少得多，特别是当平均函数在与散度矩阵的最大变化方向正交的方向上变化时。预计在其他多变量分析领域，如判别分析和功能数据分析，也会有类似的结果。包络是一种解决多元统计问题的新范式，它有可能促进解释，改进分析，否则可能是脆弱的，并且相对于标准方法在效率方面产生真正的巨大收益。许多科学领域的技术进步都伴随着多元数据的配置，这些数据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。在生命科学领域尤其如此，从复杂的数据体中提取相关信息的能力至关重要。研究者和他的同事们计划研究一类新的多元统计方法，这种方法能够有效地从复杂的数据中提取出特定目的的相关信息。例如，组织工程的首要目标是获得用体外制造的有活力的组织贴片替代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，因为体外培养的组织缺乏足够的机械完整性，无法在体内应用。组织的机械完整性是由几百个细胞间信号蛋白组成的网络控制的，这些蛋白决定了组织的长期生长，可以通过质谱法测量。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的蛋白质指标来提取相关信息，这些指标可以在体外生长过程中被监测并由外部刺激指导。

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.