Methodologies for Modeling and Analyzing Massive Environmental and Biomedical Data Sets

如今，高通量数据的出现，例如生物统计学——特别是那些与基因表达研究有关的数据——以及环境科学——例如从卫星传输的气象数据——必须得到快速分析。申请人之前提倡的基于样本矩的创新技术，或者在他的几篇论文中讨论的依赖贝叶斯方法的创新技术，应该进一步发展和适应于如此大规模的观测数据集的数据挖掘。由于复杂数据经常涉及多个变量，我还计划将我介绍的半参数单变量基于矩的密度估计技术扩展到多变量上下文中。新的多元数据可视化技术，将适合于某些类型的大型数据集也将提出。本文将现有的关于高斯和椭圆轮廓向量下奇异二次型的分布结果推广到厄米情况，推广到用随机矩阵代替随机向量的广义二次表达式。申请人在上届国际环境学会年会上介绍的二元密度估计技术，包括用边际分布的密度估计和多项式调整（其系数由矩匹配技术确定）的乘积来表示联合密度估计，将扩展到多变量设置。一旦在边际的逆分布函数上求值，这样的多项式就变成了一个联结密度。可以说，这种方法产生了人们所能设计的最灵活的交配方式。这种方法应应用于来自各种科学调查领域的庞大数据集，如环境计量学、金融建模、计量经济学和基因组研究。仅仅基于有限数量的联合样本矩，这样的技术应该被证明比核密度估计更适合于建模一系列可以被解释为“大数据”的观测，因为它们很容易以函数形式产生密度估计，从而适合代数操作。基于矩的数据挖掘方法计算简单，可以有效地帮助研究人员在大型复杂数据集中检测异常、模式和依赖关系。我还打算开发软件文档和源代码，以促进上述分发方法的实现。此外，还计划撰写关于各种二次型分布的评估以及基于矩的密度估计和近似技术的专著。

Nowadays, high throughput data arising for instance in biostatistics-especially those observed in connection with gene expression studies-and in the environmental sciences-for instance, meteorological data transmitted from satellites-must be rapidly analyzed. Innovative techniques such as those based on samples moments, which the applicant has previously advocated, or those relying on the Bayesian approach, which are discussed in several of his papers, shall be further developed and adapted to data mine such massive sets of observations. Since complex data frequently involve several variables, I also plan to extend the semi-parametric univariate moment-based density estimation techniques that I have introduced to the multivariate context. Novel multivariate data visualization techniques that would be suited to certain types of large data sets shall be proposed as well. Extant distributional results on singular quadratic forms in Gaussian and elliptically contoured vectors shall be extended to the Hermitian case and to generalized quadratic expressions, which involve random matrices in lieu of random vectors. The bivariate density estimation techniques introduced by the applicant at the last annual meeting of The International Environmentrics Society, which consists in expressing joint density estimates in terms the product of the density estimates of the marginal distributions and a polynomial adjustment whose coefficients are determined from a moment matching technique, will be extended to multivariate settings. Once evaluated at the inverse distribution functions of the marginals, such a polynomial turns out to be a copula density. This approach arguably gives rise to the most flexible type of copulae one could devise. This methodology shall be applied to colossal data sets arising from various fields of scientific investigation such as environmetrics, financial modeling, econometrics and genomic studies. Being merely based on a finite number of joint sample moments, such techniques should prove more suitable than, for instance, kernel density estimates for modeling series of observations that can be construed as "big data", as they readily produce density estimates in a functional form that lends itself to algebraic manipulations. Given their computational simplicity, moment-based data mining methods ought to efficiently assist researchers in detecting anomalies, patterns and dependencies in large and complex data sets. I also intend to develop software documentation and source code to facilitate the implementation of the aforementioned distributional methodologies. Additionally, monographs on the evaluation of the distribution of various types of quadratic forms and on moment-based density estimation and approximation techniques are planned.