Lectures for Bayesian Learning, 7.5 hp

This page contains a short description of the contents, reading instructions and additional material for each lecture.

Schedule

The course schedule can be found on TimeEdit.

Literature

• The BL listed below are section numbers from the course book Villani (2025a). Bayesian Learning.
• The BLprequel listed below are section numbers from a book Bayesian Learning - the prequel.
• The BDA listed below are section numbers from the course book Gelman, Carlin, Stern, Dunson, Vehtari, Rubin (2014). Bayesian Data Analysis.

Lecture contents

Lecture 0 (Recorded, no physical class) - The likelihood function. Information. Basic Monte Carlo simulation.
Read: BL 1.1-1.3, BL 10.1-10.3, BLprequel 8.3, 8.4, 8.6 (check that you know the concepts) | Slides
Interactive (check that you know the concepts): MLE for Bernoulli data | MLE for Poisson | Second derivative as function curvature | Likelihood and Information | Law of large numbers | Central limit theorem

Lecture 1 - Subjective probability and Bayesian learning. Bernoulli. Gaussian with known variance.
Read: BL 1.4-1.5, 2.1-2.3 | Slides
Interactive: Bayes theorem for events | Bernoulli data | Normal data - known variance

Lecture 2 - Poisson. Summarizing a posterior distribution. Priors.
Read: BL 2.2-2.5, BL 4.1-4.8 | Slides
Interactive: Poisson data | Credible intervals

Lecture 3 - Marginalization. Gaussian with unknown variance. Multinomial. Multivariate normal.
Read: BL 3.1-3.3, 3.5-3.6 | Slides
Interactive: Normal data - unknown variance | Scaled inverse chi2 | Dirichlet distribution | Multinomial data | Multivariate normal distribution

Lecture 4 - Bayesian prediction. Decision making.
Read: BL 6.1-6.2 | Slides
Interactive: Prediction of Normal data - known variance | Prior predictive distribution - Poisson model

Lecture 5 - Regression. Regularization priors.
Read: BL 5, 12.1-12.4, 12.6 | Slides
Interactive: Bayesian linear regression

Lecture 6 - Normal posterior approximation. Classification.
Read: BL 7.1-7.5, 8.1-8.5 | Slides
Interactive: Taylor approximation | Beta model for proportions

Lecture 7 - Gibbs sampling
Read: BL 9.1-9.5 | Slides
Interactive:

Lecture 8 - Metropolis-Hastings
Read: this | Slides
Interactive:

Lecture 9 - Hamiltonian Monte Carlo
Read: this | Slides
Interactive:

Lecture 10 - Probabilistic programming for Bayes
Read: this | Slides
Interactive:

Lecture 11 - Model comparison
Read: BL 14.1-14.4 | Slides
Interactive:

Lecture 12 - Course summary.
Read: this | Slides
Interactive: