Preface

About the author

This course text was written 2018–2023 by Professor Korbinian Strimmer, a member of the Statistics group at the Department of Mathematics of the University of Manchester.

Course unit leads

This course was first taught in the winter semester 2018 by Professor Korbinian Strimmer, until and including the winter semester 2023.

In autumn 2024 the lecturer of the MATH38161 module was Dr Yuk Ka Chung.

Starting in autumn 2025 the course is lead by Dr Nilabja Guha.

About the module

Topics covered

The MATH38161 module is designed to run over the course of 11 weeks. It has six parts, each covering a particular aspect of multivariate statistics and machine learning:

1. Multivariate random variables and estimation in large and small sample settings (W1 and W2)
2. Transformations and dimension reduction (W3 and W4)
3. Unsupervised learning/clustering (W5 and W6)
4. Supervised learning/classification (W7 and W8)
5. Measuring and modelling multivariate dependencies (W9)
6. Nonlinear and nonparametric models (W10, W11)

This module focuses on:

• Concepts and methods (not on theory)
• Implementation and application in R
• Practical data analysis and interpretation (incl. report writing)
• Modern tools in data science and statistics (R markdown, R studio)

Additional support material

If you are a University of Manchester student and enrolled in this module you will find on Canvas:

• a weekly learning plan for an 11 week study period,
• weekly worksheets with with examples (theory and application in R) and solutions in R Markdown, and
• exam papers of three previous years.

Furthermore, there is also an MATH38161 online reading list hosted by the University of Manchester library.

Prerequisites

Multivariate statistics relies heavily on matrix algebra and vector and matrix calculus. For a refresher of the essentials please refer to the supplementary

• Matrix and Calculus Refresher notes.

Furthermore, this module builds on earlier statistics modules, especially on likelihood estimation and Bayesian statistics as discussed, e.g., in the module

• MATH27720 Statistics 2.

For an overview of essential probability distributions see the

• Probability and Distributions Refresher notes.

Acknowledgements

Many thanks to Beatriz Costa Gomes for her help to compile the first draft of these course notes in the winter term 2018 while she was a graduate teaching assistant for this course. Thanks also to the many students who suggested corrections and found typos.