Multivariate Analysis
For honours courses please contact the School Office.
Description
Multivariate analysis of data is performed in order to
1 understand the structure in data and summarise the data in simpler ways;
2 understand the relationship of one part of the data to another part; and
3 make decisions or draw inferences based on data.
The statistical analyses of multivariate data extend those of univariate data by using interesting and challenging mathematical theory and computational techniques. The course begins with a discussion of the three classical methods Principal Component Analysis, Canonical Correlation Analysis and Discriminant Analysis which correspond to the aims above. We also learn about Cluster Analysis, Factor Analysis and newer methods including Independent Component Analysis.
For most real data the underlying distribution is not known, but if the assumptions of multivariate normality of the data hold, extra properties can be derived. Our treatment combines ideas, theoretical properties and a strong computational component for each of the different methods we
discuss. For the
computational part we make use of real data and learn the use of simulations in order to assess the performance of different methods in practice.
Objective
This course aims to familiarise students with classical and modern methods for analysing multivariate data; equip students with computational skills to implement these methods in practice; enable students to determine appropriate methods for problems in multivariate analysis; and present an overview of new directions in multivariate analysis and open research problems. To introduce students to classical and modern methods for the analysis of multivariate and high-dimensional data. At the end of the course students should have reached an understanding and overview of different ways of analysing multivariate data, have learnt how the different methods fit together; and should gained practical experience in performing analyses of large and high-dimensional data.
Content
1.Introduction to multivariate data, the multivariate normal distribution
2.Principal Component Analysis, theory and practice
3.Canonical Correlation Analysis, theory and practice
4.Discriminant Analysis, Fisher's LDA, linear and quadratic DA
5.Cluster Analysis: hierarchical and k-means methods
6.Factor Analysis and latent variables
7.Independent Component Analysis including an Introduction to Information Theory
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| Year |
Semester |
Level |
Units |
| 2012 |
1 |
Honours |
3 |
Delivery
2-hour lectures each week.
Assessment
A 3 hour exam (70% which may include 20% from a practice exam), and 30% from assignments and presentations during class.
Graduate attributes
Linkage past
No past linkages have been noted.
Linkage present
No present linkages have been noted.
Linkage future
This course is recommended for Honours students in Statistics.
Restrictions
None.
Recommended text
The course is based on the draft monograph I. Koch: `Analysis of multivariate and high-dimensional data', which will be available to students.
References:
I. T. Jolliffe: Principal Component Analysis.
K. V. Mardia, J. T. Kent and J. M. Bibby: Multivariate Analysis.
R. A. Johnson and D. W. Wichern: Applied Multivariate Statistical Analysis.
A. Hyvaerinen, J. Karhunen and E Oja: Independent Component Analysis.
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