🗓️ Week 02 - Bayesian Linear Regression

Author

Affiliation

Dr. Simone Rossi

EURECOM

In our second week, we will introduce Bayesian Linear Regression, exploring how Bayesian inference applies to linear models for regression. We will discuss what is a likelihood, a prior distribution, and their roles in Bayesian inference. We will cover key concepts such as posterior updates, model selection and model uncertainty. Additionally, we will work through practical examples to solidify understanding.

🖥️ Lecture Slides

• Bayesian Linear Regression
• Bayesian inference of coin toss experiment

📑 Lecture Notes (PDF)

• Bayesian Linear Regression
• Bayesian inference of coin toss experiment

🧪 Lab

Labs are available on GitHub (check the README file for instructions on how to run the notebooks). This week, we just recommend the following tutorial for students who are not yet comfortable with Python and NumPy:

• Tutorial 1 — Introduction to Python/NumPy (Recommended preparation before next week)

This tutorial is not mandatory (no submission required), but it is strongly recommended if you are not comfortable with Python and NumPy.

📝 Exercises

• Bayesian linear regression exercises

📚 Recommended Reading

• Murphy (2022): Chapter 11.1, 11.2, 11.3 (Linear regression)
• Murphy (2022): Chapter 11.7 (Bayesian linear regression)
• Murphy (2023): Chapter 13.2 (Bayesian linear regression)
• Murphy (2023): Chapter 3.2.1 (Coin toss exercise)

📙 References

Murphy, K. P. (2022). Probabilistic machine learning: An introduction. MIT Press. http://probml.github.io/book1

Murphy, K. P. (2023). Probabilistic machine learning: Advanced topics. MIT Press. http://probml.github.io/book2