Preface
About the module
The notes are for the version of MATH27720 Statistics 2 taught in spring 2025 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:
- Entropy and likelihood (W1–W5)
- Bayesian statistics (W6–W10)
This module focuses on conceptual understanding and methods, not on theory. Specifically, you will learn about the foundations of statistical learning using likelihood and Bayesian approaches and also how these are underpinned by entropy. The aim is to show how diverse statistical approaches are linked and to demonstrate that statistics offers a concise and coherent theory of information rather than just being a collection of “recipes” for data analysis (a common but wrong perception of statistics).
The presentation in this course is non-technical and most sections and examples will be easily accessible for a year 2 mathematics student. Sections and examples marked \(\color{Red} \blacktriangleright\) are either conceptually or technically a bit more advanced (e.g. involving more complicated matrix operations). These examples may be omitted on first reading.
If you are a University of Manchester student and enrolled in this module you will find additional support material on Blackboard:
- a weekly learning plan,
- worksheets with examples and solutions (and R code), and
- exam papers of previous years.
Furthermore, a MATH27720 Statistics 2 online reading list is hosted by the University of Manchester library.
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.