Algorithms for Applied Multivariate Statistical Analysis

该项目专注于开发、分析和实现用于计算经典随机矩阵集合（Wishart， Jacobi和Laguerre）的特征值（及其函数）分布的算法。重点是利用多元正交多项式的组合和代数性质，以及利用结构矩阵计算和动态规划技术来实现高实用效率。本研究将为多元统计技术在实践中的应用提供新的有效工具。这些技术在许多领域和应用中都是至关重要的，包括生物信息学、基因组学（种群分类）、无线通信（网络容量优化）和军事应用（自动目标分类）。

This project concentrates on the development, analysis, and implementation of algorithms for computing the distributions of the eigenvalues (and functions thereof) of the classical random matrix ensembles -- Wishart, Jacobi, and Laguerre. The focus is on achieving high practical efficiency by exploiting the combinatorial and algebraic properties of multivariate orthogonal polynomials as well as utilizing structured matrix computations and dynamic programming techniques.brbrThis research will provide new efficient tools for using multivariate statistical techniques in practice. Such techniques are critical in many areas and applications, including bioinformatics, genomics (population classification), wireless communications (network capacity optimization), and military applications (automatic target classification).