Applied Multivariate Statistics
| Code | School | Level | Credits | Semesters |
| MATH4068 | Mathematical Sciences | 4 | 20 | Spring UK |
- Code
- MATH4068
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Spring UK
Summary
This course is concerned with the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. A theme running through the module is that of dimension reduction. Key topics to be covered include:
- principal components analysis, whose purpose is to identify the main modes of variation in a multivariate dataset;
- modelling and inference for multivariate data, including multivariate regression data, based on the multivariate normal distribution;
- classification of observation vectors into subpopulations using a training sample;
- canonical correlation analysis, whose purpose is to identify dependencies between two or more sets of random variables.
Further topics to be covered include methods of clustering and multidimensional scaling.
Target Students
Available to MSc students. All other students with suitable prerequisites should take the level 3 version instead.
Classes
- Two 2-hour lectures each week for 11 weeks
Assessment
- 20% Project 1: A combination of reading relevant literature, data analysis using a suitable statistical package and preparing a report (max length: 10 pages)
- 80% Exam 1 (3-hour): Written examination.
Assessed by end of spring semester
Educational Aims
The purpose of thiscourse is to broaden the students' knowledge of statistics by introducing them to important contemporary topics in multivariate analysis. Thiscourse is in the Statistics pathway and builds upon the statistical ideas and methods of the course MATH4019. Students will acquire knowledge and skills of relevance to a professional and/or research statistician.Learning Outcomes
A student who completes this module successfully will be able to:
L1 - state and prove standard results relating to multivariate statistical theory;
L2 - derive multivariate statistical techniques such as principal component analysis, classification and canonical correlation analysis, clustering and multidimensional scaling, and understand and explain the properties of these techniques;
L3 - derive, explain and apply methods of statistical inference for multivariate data based on the multivariate normal distribution;
L5 - apply multivariate models and methods to suitable datasets using a statistical environment such as R and interpret the results;
L6 - write a report based on the analysis of a multivariate dataset;
L7 - research and synthesize a topic in multivariate analysis.