(Last Updated:03 May 2017)

**Total Credits: **20

**Level: **Level 4

**Target Students: **Open only to MSc students. All other students with suitable prerequisites should take G13MVA instead.

**Taught Semesters:**

Semester | Assessment |
---|---|

Spring | Assessed by end of Spring Semester |

**Prerequisites: **Students should be familiar with definitions,concepts&theorems relating to univariate distributions-the normal&chi-squared distributions;linear regression&analysis of variance models;parameter estimation&hypothesis testing,such as the likelihood ratio test;elementary linear algebra,such as eigenvalue/eigenvector analysis & basic matrix manipulations, including matrix multiplication&inversion.

Mnem | Title |
---|---|

G14FOS | Fundamentals of Statistics |

**Corequisites: **None.

**Summary of Content: **This module 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 factor analysis, methods of clustering and multidimensional scaling.

**Method and Frequency of Class: **

Activity | Number Of Weeks | Number of sessions | Duration of a session |
---|---|---|---|

Lecture | 12 weeks | 2 per week | 2 hours |

Activities may take place every teaching week of the Semester or only in specified weeks. It is usually specified above if an activity only takes place in some weeks of a Semester

Four hours of lectures per week, some of which may be used as problems classes, examples classes or computer workshops.

**Method of Assessment: **

Assessment Type | Weight | Requirements |
---|---|---|

Exam 1 | 80 | One 2.5hr written examination |

Project 1 | 20 | A combination of reading relevant literature, data analysis using a suitable statistical package and preparing a report (max length: 10 pages) |

**Convenor: **

Professor A Wood

**Education Aims: **The purpose of this module is to broaden the students' knowledge of statistics by introducing them to important contemporary topics in multivariate analysis. This module is in the Statistics pathway and builds upon the statistical ideas and methods of the module G14FOS. 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.

**Offering School: **Mathematical Sciences

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