課程資訊
課程名稱
多變量統計分析一
Multivariates Statistical Analysis (Ⅰ) 
開課學期
101-2 
授課對象
理學院  數學系  
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
星期一7,8(14:20~16:20)星期二7(14:20~15:10) 
上課地點
天數204天數204 
備註
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1012mva 
課程簡介影片
 
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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
 

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)
Haerdle, W. and Simar, L. (2007) Applied Multivariate Statistical Analysis [本校電子書]
 
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
  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
  Monday: Tutorial on R-program
Tuesday: PCA (Chapter 8: Introduction, Population PC)
 
第3週
03/04  Monday: population PCA, functional data
Tuesday: Multivariate Normal distribution; Matrix Algebra and Random Vectors 
第4週
  Monday and Tuesday: Chapter 4.2 Multivariate Normal Density and Its Properties Ch4.3 Estimation in MVN

 
第5週
03/18  Monday: Derive MLE and finish up Chapter 4.3-4.6
Tuesday: Finish Chapter 4.
 
第6週
3/25  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
4/01  Monday, Tuesday 
第8週
4/08  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
4/15  Monday: Finish up EM
未教MANOVA, Profile analysis, and growth curves 
第10週
4/22 
 
第11週
4/29  Monday & Tuesday: EM algorithm and Likelihood Ratio test 
第12週
5/06  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
5/13  Monday: PCA Tuesday: Factor Analysis 
第14週
5/20  Monday: Factor Analysis; Tuesday: Canonical Correlation Analysis

 
第15週
5/27  Monday: Canonical Correlation Analysis; Tuesday: Clustering 
第16週
6/03  Monday: Discrimination and Classification
 
第17週
6/10  Monday: Clustering
Tuesday: Review 
第18週
6/17  Tuesday: Final (open book exam)