Laurea Magistrale (M.Sc.) in Stochastics and Data Science

MULTIVARIATE STATISTICAL ANALYSIS

MULTIVARIATE STATISTICAL ANALYSIS

Academic year 2015/2016

Sommario del corso

• Course objectives
• Results of learning outcomes
• Course delivery
• Learning assessment methods
• Program
• Suggested textbooks and readings
• Teaching tools

Course objectives

Results of learning outcomes

The student will learn the basic techniques for analyzing multi-dimensional data (including visualization), study multivariate distributions and their properties, discuss various methods for dimension reduction.

Course delivery

The course is composed of 48 hours of class lectures. Examples and exercises will be dealt with at class through the R language.

Learning assessment methods

Problem Sets:
There will be 2/3 problem sets assigned throughout the course.  They will be posted in due time on
https://sites.google.com/a/carloalberto.org/pdeblasi/teaching
together with an indication of the deadline.
Problem sets must be submitted and there are no late submissions. They are an essential part of the course, providing students with a guide on how well they are grasping the material on a “real time” basis. They request the solution of two or more exercises, solution which might require the use of a statistical software. Students are encouraged to work in groups on the problem sets. However, students should understand the material on their own, and hand in their own problem sets.


Exam:
There will be a final exam, check out for dates on
http://www.master-sds.unito.it
The final examination includes a written or an oral test according to the problem sets.
Specifically, in the first 2 exam dates, the grade will be determined either by
(1.1) problem session (50%)
(1.2) final exam via oral test (50%)
or by
(2) final exam via written test (100%)
for students who have failed to submit the problem sets. From 3rd exam date on, only case (2) above applies.

Program

- Introduction
       - summary statistics for multivariate data
       - multivariate data visualization
       - multivariate Normal distributions
- Principal Component Analysis (PCA):
       - geometric and algebraic basics of PCA
       - calculation and choice of components
       - plotting PCs, interpretation
- Factor Analysis (FA):
       - model definition and assumptions
       - estimation of loadings and communalities
       - choice of the number of factors
       - factor rotation
- Canonical Correlation Analysis:
       - computation and interpretation
       - relationship with multiple regression
- Discriminant Analysis and Classification:
       - classification rules
       - linear and quadratic discrimination
       - error rates
- Cluster Analysis:
       - measure of similarity
       - hierarchical clustering
       - K-means clustering
       - model based clustering

The bibliography, to be confirmed at the beginning of the course, is:

- R.A. Johnson and D.W. Wichern (2007). Applied Multivariate Statistical Analysis. Prentice-Hall, 6th Ed.

Suggested readings:
- Afifi A., May S., Clark V.A. (2012). Practical Multivariate Analysis, 5th ed., Chapman & Hall/CRC
- Everitt B. (2005). An R and S-PLUS Companion to Multivariate Analysis. Springer
- Rencher A. C., Christensen W. F. (2012). Methods of multivariate analysis, 3rd ed., Wiley
- Rencher A.C. (1992). Interpretation of canonical discriminant functions, canonical variates and principal components. The American Statistician 46, 217-225.

Class schedule

• Teaching materials
• Exams and finals
• Go to Moodle
• Visit the forums