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Statistical Methods: Likelihood, Bayes and Regression

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.

The notes are for the version of MATH20802 taught in spring 2023 at the University of Manchester.

I hope that you enjoy the course and that you will find the notes useful! If you have any questions, comments, or corrections please email me at .

About the module

Topics covered

The MATH20802 module is designed to run over the course of 11 weeks. It has three main parts:

  1. Likelihood estimation and inference (W1–W4)
  2. Bayesian learning and inference (W5–W8)
  3. Linear regression (W9–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.

As such, the presentation in this course is non-technical. 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 an adhoc collection of “recipes” for data analysis (a common but wrong perception of statistics).

Prerequisites

For this module it is important that you refresh your knowledge in:

  • Introduction to statistics
  • Probability
  • R data analysis and programming

In addition you will need to some elements of matrix algebra and how to compute the gradient and the curvature of a function of several variables.

Check the Appendix of these notes for a brief refresher of the essential material.

Additional support material

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

  • a weekly learning plan for an 11 week study period (plus one additional week for revision),
  • weekly worksheets with examples and solutions and R code, and
  • exam papers of previous years.

Furthermore, there is also a MATH20802 online reading list hosted by the University of Manchester library.

The future

The year 2 MATH20802 “Statistical Methods” module (10 credits) is last run in the academic year 2022/23.

From 2023/24 onwards the likelihood and Bayes parts of this module will be delivered as part 2 of the new year 2 module MATH27720 “Probability and Statistics 2” (20 credits). Linear regression will be taught in the new year 2 module MATH27711 “Linear regression models” (10 credits).

Acknowledgements

Many thanks to Beatriz Costa Gomes for her help in creating the 2019 version of the lecture notes when I was teaching this module for the first time and to Kristijonas Raudys for his extensive feedback on the 2020 version.