Preface

About the author

Hello! My name is Korbinian Strimmer and I am a Professor in Statistics. I am a member of the Statistics group at the Department of Mathematics of the University of Manchester. You can find more information about me on my home page.

About the module

The notes are for the version of MATH27720 Statistics 2 taught in spring 2024 at the University of Manchester.

The MATH27720 Statistics 2 module is designed to run over the course of 11 weeks. It has the following structure:

  1. Introduction and refresher (W1)
  2. Likelihood estimation and inference (W2–W5)
  3. Bayesian learning and inference (W6–W10)
  4. Revision (W11)

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 offer insights how diverse statistical approaches are linked and to demonstrate that statistics offers a concise and coherent theory of information rather than being a collection of “recipes” for data analysis (a common but wrong perception of statistics).

The presentation in this course and notes is non-technical and most sections and examples should be easily accessible for a year 2 mathematics student. Some sections and examples (marked \({\color{Red} \blacktriangleright}\)) are either conceptually or technically more advanced. These will deepen the overall understanding but 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 for an 11 week study period (including one week for revision),
  • worksheets with examples and solutions and R code, and
  • exam papers of previous years.

Furthermore, there is also a MATH27720 Statistics 2 online reading list 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.