2008/09 Undergraduate Module Catalogue
MATH3772 Multivariate Analysis
10 creditsClass Size: 100
Module manager: Dr S. Barber
Email: stuart@maths.leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2008/09
Pre-requisite qualifications
MATH2715 or MATH2735.This module is mutually exclusive with
| MATH5772M | Multivariate and Cluster Analysis |
This module is 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. For example, reducing the effective number of variables as in principal components analysis, describing the structure of dependence between variables as in factor analysis and classifying observation to populations as in descriminant 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. Principal component analysis; dimension reduction; covariance vs. correlation matrix.
6. Factor analysis; common and specific factors; Heywood cases; interpretation of factor loadings; determination of number of factors.
7. Discriminant analysis; maximum likelihood and Bayesian discriminant rules for normal data; misclassification probabilities and assessment by cross- validation; Fisher's discriminant rule.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| Example Class | 4 | 1.00 | 4.00 |
| Lecture | 18 | 1.00 | 18.00 |
| Practical | 2 | 1.00 | 2.00 |
| Private study hours | 76.00 | ||
| Total Contact hours | 24.00 | ||
| Total hours (100hr per 10 credits) | 100.00 | ||
Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| In-course Assessment | . | 20.00 |
| Total percentage (Assessment Coursework) | 20.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Exams
| Exam type | Exam duration | % of formal assessment |
| Standard exam (closed essays, MCQs etc) | 2 hr | 80.00 |
| Total percentage (Assessment Exams) | 80.00 | |
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 websiteLast updated: 11/03/2009
Browse Other Catalogues
- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue
Errors, omissions, failed links etc should be notified to the Catalogue Team.PROD