Introductory description

This module runs in Term 1 and is an optional module intended for students in their third or fourth year of study who have previously taken preparatory modules in Statistics.

Pre-requisites

• Statistics Students:

  • ST218 Mathematical Statistics A; or,
  • ST228 Mathematical Methods for Statistics and Probability and ST229 Probability for Mathematical Statistic.

• Non-Statistics Students:

  • ST220/ST226 Introduction to Mathematical Statistics; or,
  • ST232/ST233 Introduction to Mathematical Statistics.

The coursework uses the statistical software package R, so knowledge in R such as covered in ST117 Introduction to Statistical Modelling/ST231 Linear Statistical Modelling with R, ST121 Statistical Laboratory or ST952 Introduction to Statistical Practice is expected.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Multivariate data arises whenever several interdependent variables are measured simultaneously. Such high-dimensional data is becoming the rule, rather than the exception in many areas: in medicine, in the social and environmental sciences and in economics. The analysis of such multidimensional data often presents an exciting challenge that requires new statistical techniques which are usually implemented using computer packages. This module aims to give you a good understanding of the geometric and algebraic ideas that these techniques are based on, before giving you a chance to try them out on some real data sets.

The module's advanced topic will include material for independent study and assessment This material will reflect current trends, innovations or expertise in the area.

Learning outcomes

By the end of the module, students should be able to:

• Construct and interpret graphical representations of multivariate data
• Carry out a principal components and canonical correlation analysis to summarise high dimensional data
• Perform clustering analysis to discover and characterize subgroups in the population.
• Use classification and discrimination methods to assign individuals into groups.
• Assess multivariate normality and do multivariate tests for comparing means across groups
• Understand any additional topics covered in the lectures. Time permitting, lectures will cover one or two additional topics such as Factor Analysis, Multidimensional Scaling, random forests, bagging, sparse multivariate methods, Gaussian graphical models, multiple testing, functional data analysis, spatial statistics.
• Understand by independent study an additional advanced topic in multivariate statistics.

Indicative reading list

Johnson, R. A., & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis.: Pearson Prentice Hall. Upper Saddle River, NJ.
James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112). New York: Springer.
Friedman, J., Hastie, T., & Tibshirani, R. (2009). The elements of statistical learning (second edition). New York: Springer.
Efron, B., & Hastie, T. (2016). Computer age statistical inference (Vol. 5). Cambridge University Press.
Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical learning with sparsity: the lasso and generalizations. CRC press.

View reading list on Talis Aspire

Subject specific skills

• Demonstrate facility with rigorous statistical methods.

• Evaluate, select and apply appropriate mathematical and/or statistical techniques.

• Demonstrate knowledge of and facility with formal probability concepts, both explicitly and by applying them to the solution of problems.

• Create structured and coherent arguments communicating them in written form. 

• Construct logical arguments with clear identification of assumptions and conclusions.

• Reason critically, carefully, and logically and derive (prove) mathematical results.

Transferable skills

• Problem solving: Use rational and logical reasoning to deduce appropriate and well-reasoned conclusions. Retain an open mind, optimistic of finding solutions, thinking laterally and creatively to look beyond the obvious. Know how to learn from failure.

• Self awareness: Reflect on learning, seeking feedback on and evaluating personal practices, strengths and opportunities for personal growth.

• Communication: Present arguments, knowledge and ideas, in a range of formats.

• Professionalism: Prepared to operate autonomously. Aware of how to be efficient and resilient. Manage priorities and time. Self-motivated, setting and achieving goals, prioritising tasks.