# Statistical Methods:

Likelihood, Bayes and Regression

Likelihood, Bayes and Regression

*MATH20802*

Lecture Notes

Lecture Notes

*Korbinian Strimmer*

University of Manchester

University of Manchester

*6 March 2021*

# Preface

## About these notes

This is the course text for MATH20802, an introductory course in **Statistical Methods** for second year mathematics students.

These notes will be updated from time to time. To view the current version in your browser visit the online MATH20802 lecture notes. You may also download the MATH20802 lecture notes as PDF.

## About the module

### Topics covered

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

- Likelihood estimation and likelihood ratio tests (W1–W5)
- Bayesian learning and inference (W6–W8)
- Linear regression (W9–W11)

This module focuses on conceptual understanding and methods, not on theory, 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 know matrix algebra and how to compute the gradient and the curvature of a function of several variables.

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

### Additional support material

Accompanying these notes are

- a weekly learning plan for an 11 week study period,
- corresponding worksheets with examples,
- lecture videos (visualiser style).

Organisatorical information is available from the course home page and on Blackboard.

If you are a University of Manchester student and enrolled for this module you can find the exam questions of previous years (without solution) as well as the info about the midterm test on Blackboard.

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

## Acknowledgements

Many thanks to Beatriz Costa Gomes for her help in creating the 2019 version of the lecture notes and to Kristijonas Raudys for his extensive feedback on the 2020 version.