課程資訊

Multivariates Statistical Analysis (Ⅰ)

101-2

MATH7607

221 U0730

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1012mva

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

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.

Solid knowledge on calculus, probability and statistics.
Familiarity with linear algebra.

Office Hours

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]

Flury, B. (1997) A First Course In Multivariate Statistics. Springer.
Srivastava, M. S. (2002) Methods of Multivariate Statistics. Wiley

(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)