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School of Mathematics

# MATH38062 - 2008/2009

General Information
• Title: Multivariate Statistical Methods
• Unit code: MATH38062
• Credits: 10
• This course unit may not be taken as well as MATH48062.
• Prerequisites: MATH20701, MATH20802
• Co-requisite units: None
• School responsible: Mathematics
• Members of staff responsible: Dr. P. Foster
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## Specification

### Aims

To familiarise students with the ideas and methodology of certain multivariate methods together with their application in data analysis.

### Brief Description of the unit

In practice most sets of data are multivariate in that they consist of observations on several different variables for each of a number of individuals or objects. Indeed, such data sets arise in many areas of science, the social sciences and medicine and techniques for their analysis form an important area of statistics. This course unit introduces a number of techniques, some of which are generalisation of univariate methods, while others are completely new (e.g. principal component analysis).

### Learning Outcomes

On successful completion of this course unit students will

• be familiar with multivariate random vectors and their probability distributions;
• have acquired skills in summarising multivariate data, dimensionality reduction techniques, inferential methods based on the multivariate Normal distribution as an underlying model and data classification techniques.

### Future topics requiring this course unit

This course unit forms a useful background to other statistics course units.

### Syllabus

1. Introductory ideas and concepts, simple graphical presentations, measuring distance, cluster analysis. [6]
2. Dimensionality reduction: Principal component analysis. [4]
3. The Multivariate Normal (MVN) distribution: Definition. Properties. The Wishart and Hotelling T2 distributions. Maximum likelihood estimation of the mean vector and covariance matrix. [4]
4. Hypothesis testing and confidence regions (1 and 2 sample procedures). [8]

### Textbooks

• Chatfield, C. and Collins, A. J., An Introduction to Multivariate Analysis, Chapman & Hall 1983.
• Krzanowski, W. J., Principles of Multivariate Analysis: A User's Perspective, Oxford University Press 1990.
• Johnson, R. A. and Wichern, D. W., Applied Multivariate Statistical Analysis 3rd edition, Prentice Hall 1992.

### Teaching and learning methods

Two lectures and one examples class each week. In addition students should expect to spend at least four hours each week on private study for this course unit.

### Assessment

Coursework: weighting 20%
End of semester examination: two hours weighting 80%

## Arrangements

On-line course materials for this course unit.