Introductory description

This module runs 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 AND ST219 Mathematical Statistics B; or
  • ST228 Mathematical Methods for Statistics and Probability, and ST229 Probability for Mathematical Statistics, and ST230 Mathematical Statistics.

• Non-Statistics Students:

  • ST104 Statistical Laboratory and ST220 Introduction to Mathematical Statistics; or,
  • ST121 Statistical Laboratory. and ST232/ST233 Introduction to Mathematical Statistics.

The coursework uses the statistical software package R, so knowledge of R such 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 and rigorous 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.

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 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.
• Conduct inference for multivariate means, construct confidence regions, and understand their potential uses, such as for group comparisons.
• 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, independent component analysis, compositional data analysis, canonical correlation analysis.

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.