2024/25 Taught Postgraduate Module Catalogue

MATH3772 Multivariate Analysis

10 Credits Class Size: 80

Module manager: Dr. Arief Gusnanto
Email: A.Gusnanto@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

Pre-requisite qualifications

MATH2715

Mutually Exclusive

This module is not approved as an Elective

Module summary

This module introduces the statistical methodology used in analysing multivariate observations, and applications to real data sets.

Objectives

To introduce the statistical methodology used in analysing multivariate observations, and to understand its application to real data sets.

On completion of this module, students should be able to:
(a) relate joint, marginal and conditional distributions and their properties with particular reference to the multivariate normal distribution;
(b) obtain and use Hotelling's T2 statistic for the one sample and two samples problems;
(c) derive, discuss the properties of, and interpret principal components;
(d) use the factor analysis model, and interpret the results of fitting such a model;
(e) derive, discuss the properties of, and interpret decision rules in discriminate analysis;
(f) use a statistical package with real data to facilitate an appropriate analysis and write a report giving and interpreting the results.

Syllabus

In multivariate analysis several variables are measured on each individual in the sample. The multivariate normal distribution now plays the same modelling role that the normal distribution does in univariate theory. Many of the univariate results have multivariate analogues and the module will look at generalisation of the t-test and confidence intervals.

But a range of new techniques become available in the multivariate setting. Such as, reducing the effective number of variables as in principal components analysis and classifying observation to populations as in discriminant analysis.

Using the computer to do these analyses and look at examples will form an integral part of the course.

Topics covered include:
1. Introduction to multivariate analysis and review of matrix algebra.
2. Multivariate distributions; moments; conditional and marginal distributions; linear combinations.
3. Multivariate normal and Wishart distributions; maximum likelihood estimation.
4. Hotelling's T2 test; likelihood vs. union-intersection approach; simultaneous confidence intervals.
5. Dimension reduction; principal component and factor analysis; covariance vs. correlation matrix; loading interpretation.
6. Discriminant analysis; maximum likelihood and Bayesian discriminant rules; misclassification probabilities and estimation; Fisher's discriminant rule.

Teaching Methods

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular problem solving assignments

Methods of Assessment

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading List

The reading list is available from the Library website

Last updated: 11/19/2024

Errors, omissions, failed links etc should be notified to the Catalogue Team