課程資訊
課程名稱
多變量統計分析一
MULTIVARIATES STATISTICAL ANALYSIS (I) 
開課學期
98-2 
授課對象
理學院  數學研究所  
授課教師
陳宏 
課號
MATH7607 
課程識別碼
221 U0730 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期一3,4(10:20~12:10)星期二2(9:10~10:00) 
上課地點
新402新402 
備註
總人數上限:35人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/982mva 
課程簡介影片
 
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課程概述

1. Introduction of Multivariate Analysis
2. Matrix Algebra, Random Vectors, and Multivariate Normal
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
 

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.  
預期每週課後學習時數
 
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)
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Homework 
30% 
 
2. 
Midterm 
30% 
 
3. 
Final  
30% 
 
4. 
Quiz 
10% 
 
 
課程進度
週次
日期
單元主題
第1週
02/22  Monday: Introduction of Multivariate Analysis; 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
03/01  Monday: Classification
Tuesday: Tutorial on R-program
 
第3週
03/08  Monday: Classification, Clustering and Mixture Distribution, Approaches on classification (Bayes risk, logistic regression, minimize misclassification error with prescribed classifier)
Tuesday: Multivariate Normal distribution; Matrix Algebra and Random Vectors 
第4週
03/15  Monday and Tuesday: Chapter 4.2 Multivariate Normal Density and Its Properties Ch4.3 Estimation in MVN

 
第5週
03/22  Monday: Derive MLE and finish up Chapter 4.3-4.6
Tuesday: Finish Chapter 4.
 
第6週
03/29  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
04/05  Monday, Tuesday溫書假 
第8週
04/12  Monday: EM algorithm
Tuesday: Quiz 1 (matrix manipulation, lagrange multiplier)
Please refer to http://episte.math.ntu.edu.tw/entries/en_lagrange_mul/index.html on idea of Lagrange multiplier
 
第9週
04/19  Monday: Finish up EM
Tuesday: Start on MANOVA, Profile analysis, and growth curves 
第10週
04/26  Monday: Midterm
Tuesday: MANOVA, Profile analysis, and growth curves 
第11週
05/03  Monday & Tuesday: PCA 
第12週
05/10  Monday & Tuesday: Discrimination and Classification  
第13週
05/17  Monday: Discrimination and Classification; Tuesday: Factor Analysis 
第14週
05/24  Monday: Factor Analysis; Tuesday: Canonical Correlation Analysis

 
第15週
05/31  Monday: Canonical Correlation Analysis; Tuesday: Clustering 
第16週
06/07  Monday: Quiz 2;
Tuesday: Clustering 
第17週
06/14  Monday: Clustering
Tuesday: Review 
第18週
06/21  Monday: Final