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MULTIVARIATE STATISTICAL ANALYSIS
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MULTIVARIATE STATISTICAL ANALYSIS
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Academic year 2015/2016
- Course ID
- MAT0041
- Teacher
- Pierpaolo De Blasi
- Year
- 1st year
- Teaching period
- Second semester
- Type
- D.M. 270 TAF C - Related or integrative
- Credits/Recognition
- 6
- Course disciplinary sector (SSD)
- SECS-S/01 - statistica
- Delivery
- Class Lecture
- Language
- English
- Attendance
- Mandatory
- Type of examination
- Oral
- Prerequisites
- Probability Theory
- Propedeutic for
- Statistical Machine Learning
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Sommario del corso
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Course objectives
The course aims at introducing multivariate analysis in statistical modeling. All the methods will be implemented on real dataset in the R language.
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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.
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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.
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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.- Oggetto:
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 clusteringSuggested readings and bibliography
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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.- Oggetto:
Class schedule
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