Preface
About the module
The notes are intended for the MATH27720 Statistics 2 course being taught in spring 2026 at the University of Manchester.
The MATH27720 Statistics 2 module is designed to run over the course of 10 weeks. It has the following two-part structure:
- Models, information and likelihood (W1–W5)
- Bayesian statistics (W6–W10)
In this course you’ll study the foundations of statistical learning using both likelihood and Bayesian approaches.
The module focuses on conceptual understanding and is presented in a nontechnical way. Most sections and examples will be accessible to a second-year mathematics or computer science student. Items labelled \(\color{Red} \blacktriangleright\) are conceptually or technically more involved and can be skipped on a first reading.
If you are a student at University of Manchester enrolled in this module, you will find additional support material on Canvas:
- a weekly learning plan,
- worksheets with examples and solutions (and R code), and
- exam papers of previous years.
Furthermore, a MATH27720 online reading list is hosted by the University of Manchester library.
In a nutshell, the two key aims of the MATH27720 Statistics 2 module are
- to provide a principled introduction to maximum likelihood and Bayesian statistical analysis and
- to show that statistics is a coherent, well founded theory of information, not merely a set of disconnected “recipes” for data analysis.
The first part of the module (Weeks 1–5) explores the method of maximum likelihood drawing on relevant aspects of information theory with application to standard models such as exponential families.
The second part of this module (Weeks 6–10) focuses on the Bayesian approach to statistical estimation and inference, presented as a natural extension of likelihood-based methods that addresses some limitations of maximum likelihood.
Acknowledgements
These notes are based in part on my earlier notes for MATH20802 Statistical Methods which was last run in Spring 2023. Many thanks to Beatriz Costa Gomes for her help in creating the 2019 version of the lecture notes when I was teaching the MATH20802 module for the first time and to Kristijonas Raudys for his extensive feedback on the 2020 version.