课程代码：120313B                                               Course Code：120313B

课程名称：多元统计分析                                       Course Name：Multivariate Statistics

学时：48=32+16                                                     Periods：48=32+16

学分：3                                                                  Credits：3

考核方式：考查                                                     Assessment：Evaluation

先修课程：《线性代数》                                       Preparatory Courses：Linear Algebra

《概率统计》                                      Probability and Statistics

多元统计分析是数理统计学中近年来发展迅速的一个分支。尤其是电子计算机的普及与软件的使用，多元分析的方法已广泛应用于各个领域。《多元统计分析》是应用数学专业的一门专业必修课程，本课程包括实验。主要使用SPSS并辅之以R等软件，实现多元分析诸多方法的计算。通过上机实验，学生们对于深奥的理论有了更深入的理解。

主要内容包括：理论上掌握多元正态分布及其他三大分布——Wishart分布、Hotelling T2分布和Wilks Λ分布，完成均值向量的假设检验（MOVOVA）并学会多元数据的图展示;掌握经典的几个方法——聚类分析和判别分析，因子分析及主成分分析和对应分析的计算,通过编程，来对典型相关分析求解。实验数据除了来自于教材以及参考书的数据之外，还有来自于学生自己搜集的感兴趣的研究领域的数据，并让学生尝试写一篇课程论文，从而培养学生提出问题、应用多元分析方法解决实际问题的能力。

Multivariate Statistics is, recently, a rapidly growing branch of Mathematical Statistics. With the widespread using of computers and software, methods of multivariate analysis has being widely used in various fields. 《Multivariate Statistics》is a professional required course for students of the applied mathematical department, which includes experiments to realize computations of the multivariate analysis methods by using SPSS and R software. Through the experiments, students will deeply understand the difficult and abstract theories.

This course covers the theoretical foundations of multivariate statistics——The Multivariate Normal Distribution and other three related distributions——Wishart distribution, Hotelling T2distribution and  Wilks Λdistribution, Multivariate Analysis of Variance (MANOVA) and learning to express multivariate data with graphs; mastering the classical methods——Clustering analysis and Discriminant Analysis, Factor analysis and Principal Component Analysis, and Correspondence Analysis, solving Canonical Correlation during programming. The experiment data are gained from the teaching material and the reference material, and also collected by students from their interesting research fields. After experiments, students will be required to write a course work, which can train the ability to propose questions and to resolve practical problems with applied multivariate analysis methods.