Module manager: Dr J P Gosling
Email: j.p.gosling@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2011/12
MATH2715 or MATH2735.
| MATH3772 | Multivariate Analysis |
This module is not approved as an Elective
By the end of this module, students should be able to:
- relate joint, marginal and conditional distributions and their properties with particular reference to the normal distribution;
- obtain and use Hotelling's T-squared statistic for the one sample and two sample problems;
- derive, discuss the properties of, and interpret principal components;
- use the factor analysis model, and interpret the results of fitting such a model;
- derive, discuss the properties of, and interpret decision rules in discriminant analysis;
- use hierarchical methods on similarity or distance matrices to partition data into clusters;
- use multidimensional scaling to construct low-dimensional representations of data;
- use a statistical package with real data to facilitate an appropriate analysis and write a report giving and interpreting the results.
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.
8. Cluster analysis, similarity matrix, distance matrix, hierarchical methods.
9. Multidimensional scaling, metric scaling, nonmetric scaling, horseshoe effect.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 33 | 1 | 33 |
| Practical | 1 | 2 | 2 |
| Private study hours | 115 | ||
| Total Contact hours | 35 | ||
| Total hours (100hr per 10 credits) | 150 | ||
Regular problem solving assignments
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | Coursework | 20 |
| Total percentage (Assessment Coursework) | 20 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 30 Mins | 80 |
| Total percentage (Assessment Exams) | 80 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 2/27/2012
Errors, omissions, failed links etc should be notified to the Catalogue Team