課程資訊
課程名稱
多變量統計分析
Multivariates Statistical Analysis 
開課學期
102-2 
授課對象
理學院  應用數學科學研究所  
授課教師
陳宏 
課號
MATH7610 
課程識別碼
221 U6160 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期一7,8星期二7 
上課地點
天數101天數101 
備註
總人數上限:30人
外系人數限制:10人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1022mva 
核心能力關聯
本課程尚未建立核心能力關連
課程大綱
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課程概述

1. Introduction of Multivariate Analysis
2. Multivariate Random Variables: Matrix Algebra, Random Vectors, Quadratic Forms, and Multinormal Distribution
3. Statistical Inferences for Multivariate Distributions
4. Principal component Analysis
5. Factor Analysis
6. Discriminant Analysis
7. Cluster Analysis
8. Multivariate Analysis of Variance
9. Canonical Correlation Analysis
10. High-dimensional Data
 

課程目標
1. Learn basic techniques for analysis of multi-dimensional data.
2. Study multivariate distributions, especially Gaussian distribution.
3. Understand multivariate statistical inference and applications such as
discriminant analysis and cluster analysis.
4. Discuss various methods for dimension reduction, including principal component
analysis, factor analysis, Canonical Correlation Analysis, etc. 
課程要求
Solid knowledge on calculus, probability and statistics.
Familiarity with linear algebra.  
Office Hours
 
參考書目
Flury, B. (1997) A First Course In Multivariate Statistics. Springer.
Srivastava, M. S. (2002) Methods of Multivariate Statistics. Wiley
 
指定閱讀
Johnson, R.A. and Wichern, D.W. (2007) Applied Multivariate Statistical
Analysis. Pearson Prentice Hall. (textbook)
Haerdle, W. and Simar, L. (2007) Applied Multivariate Statistical Analysis [本校電子書]
Izenman, A. (2008) Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning [本校電子書]
Everitt, B. and Hothorn, T. (2011) An Introduction to Applied Multivariate Analysis with R [本校電子書]
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Quiz 
10% 
 
2. 
Final  
30% 
 
3. 
Midterm 
30% 
 
4. 
Homework 
30% 
 
 
課程進度
週次
日期
單元主題
第1週
02/17, 02/18  Monday: Talk about examples on using PCA and the philosophy of my teaching. Start with algorithm aspect of Principal component Analysis Tuesday: Finish algorithm aspect of PCA and remind students to study Chapter 2 on Matrix Algebra and Random Vector 
第2週
02/24, 02/25  Monday: Tutorial on R-program Tuesday: PCA (Chapter 8: Introduction, Population PC)  
第3週
03/03, 03/04  Monday: population PCA, functional data Tuesday: Multivariate Normal distribution; Matrix Algebra and Random Vectors 
第4週
03/10, 03/11  Monday and Tuesday: Chapter 4.2 Multivariate Normal Density and Its Properties Ch4.3 Estimation in MVN  
第5週
03/17, 03/18  Monday: Derive MLE and finish up Chapter 4.3-4.6 Tuesday: Finish Chapter 4.  
第6週
03/24, 03/25  Monday: Chapter 5.1-5.6; Tuesday: Finish Chapter 5 and EM algorithm. Comparisons of Several Multivariate Means (profile analysis, growth curve) 
第7週
03/31, 04/01  Monday, Tuesday 
第8週
04/07, 04/08  Monday: EM algorithm Tuesday: Class is cancelled. Please refer to http://episte.math.ntu.edu.tw/entries/en_lagrange_mul/index.html on idea of Lagrange multiplier  
第9週
04/14, 04/15  Monday: 期中考 Finish up EM 未教MANOVA, Profile analysis, and growth curves 
第11週
04/28, 04/29  Monday & Tuesday: EM algorithm and Likelihood Ratio test 
第12週
05/05, 05/06  Monday & Tuesday: Tuesday: midterm (15:30 to 17:20); It covers materials from Chapters 1-4, Chapter 5:1-4, Chapter 5:7 (EM algorithm) and Chapter 8:1-2.  
第13週
05/12, 05/13  Monday: Support Vector Machine Tuesday: Factor Analysis 
第14週
05/19, 05/20  Monday: Factor Analysis; Tuesday: Canonical Correlation Analysis  
第15週
05/26, 05/27  Monday: Canonical Correlation Analysis; Tuesday: Clustering 
第16週
06/02, 06/03  Monday: 端午節 (放假日)Tuesday: Discrimination and Classification  
第17週
06/09, 06/10  Monday: Clustering Tuesday: Review 
第18週
06/16  Monday: Final (open book exam)