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課程名稱 |
多變量統計分析一
Multivariates Statistical Analysis (Ⅰ) |
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開課學期 |
101-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
陳 宏 |
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課號 |
MATH7607 |
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課程識別碼 |
221 U0730 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一7,8(14:20~16:20)星期二7(14:20~15:10) |
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上課地點 |
天數204天數204 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1012mva |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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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
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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. |
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課程要求 |
Solid knowledge on calculus, probability and statistics.
Familiarity with linear algebra. |
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預期每週課後學習時數 |
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Office Hours |
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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]
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參考書目 |
Flury, B. (1997) A First Course In Multivariate Statistics. Springer.
Srivastava, M. S. (2002) Methods of Multivariate Statistics. Wiley
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
30% |
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2. |
Midterm |
30% |
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3. |
Final |
30% |
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4. |
Quiz |
10% |
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週次 |
日期 |
單元主題 |
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第1週 |
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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 |
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第2週 |
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Monday: Tutorial on R-program
Tuesday: PCA (Chapter 8: Introduction, Population PC)
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第3週 |
03/04 |
Monday: population PCA, functional data
Tuesday: Multivariate Normal distribution; Matrix Algebra and Random Vectors |
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第4週 |
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Monday and Tuesday: Chapter 4.2 Multivariate Normal Density and Its Properties Ch4.3 Estimation in MVN
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第5週 |
03/18 |
Monday: Derive MLE and finish up Chapter 4.3-4.6
Tuesday: Finish Chapter 4.
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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) |
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第7週 |
4/01 |
Monday, Tuesday |
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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
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第9週 |
4/15 |
Monday: Finish up EM
未教MANOVA, Profile analysis, and growth curves |
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第10週 |
4/22 |
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第11週 |
4/29 |
Monday & Tuesday: EM algorithm and Likelihood Ratio test |
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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. |
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第13週 |
5/13 |
Monday: PCA Tuesday: Factor Analysis |
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第14週 |
5/20 |
Monday: Factor Analysis; Tuesday: Canonical Correlation Analysis
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第15週 |
5/27 |
Monday: Canonical Correlation Analysis; Tuesday: Clustering |
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第16週 |
6/03 |
Monday: Discrimination and Classification
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第17週 |
6/10 |
Monday: Clustering
Tuesday: Review |
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第18週 |
6/17 |
Tuesday: Final (open book exam) |
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