Outline

Instructor

Course details

Course content

Hands on introduction to Bayesian data analysis. The course will cover the formulation, evaluation and comparison of Bayesian models through examples.

Mathematical review. Basics of Markov Chain Monte Carlo methods and sampling algorithms, with a focus on off the shelf software (e.g., Stan, INLA). Approximation methods. Hierarchical modelling, with a focus on latent Gaussian models.

Themes covered:

  • Introduction to the Bayesian paradigm
  • Formulation, comparison and evaluation of Bayesian models
  • Sampling algorithms and Markov chain Monte Carlo methods
  • Computational strategies for inference
  • Hierarchical models
  • Advanced topics

Target audience and prerequisites

The course is part of the PhD program in Administration offered by HEC Montréal jointly with McGill, Concordia and Université du Québec à Montréal (UQÀM). Other Québec students can register via BCI.

Course materials

I will provide slides and videos. In addition to those, there will be assigned readings from textbook and reference papers.

Textbooks

Course notes for the class can be found online

I also recommend the following four references (Gelman et al., 2026; Held & Bové, 2020; Villani, 2025), which most closely follow the content and philosophy of the course.

  • A. Gelman, A. Vehtari, R. McElreath et al. (2026). Bayesian Workflow, Chapman and Hall (website).
  • M. Villani Bayesian Learning book (work in progress).
  • L. Held and D. Sabanés Bové (2020). Likelihood and Bayesian Inference With Applications in Biology and Medicine, 2nd edition, Springer, doi:10.1007/978-3-662-60792-3

Additional references include Gelman et al. (2013), McElreath (2020) and Johnson et al. (2022).

Other references

There will occasionally be additional articles to read; links to these other resources will be included on the content page for that session.

Course content

Below is a tentative schedule.

Week 1: Tools of the trade

  • Marginalization and conditioning
  • Review of probability distributions
  • Likelihood
  • Monte Carlo integration

See Bayesian learning: the prequel by Mathias Villani.

Week 2: Basics of Bayesian inference

  • Key concepts: prior, posterior and interpretation
  • Predictive distributions
  • Marginal likelihood and numerical integration
  • Credible intervals, loss functions and posterior summaries
  • The beta binomial conjugate model

Week 3: Prior beliefs

  • Conjugate priors
  • Flat and vague priors.
  • Priors for scale parameters
  • Parameter elicitation and expert knowledge
  • Penalized complexity prior
  • Prior sensitivity analysis

Evaluations and assessment

Your final grade will be based on assignments, a midterm and a final examination. All evaluations are individual work.

There will be weekly exercises, which we will discuss at the beginning of the next class. These are for practice and will not be graded, although you are welcome to request feedback.

The midterm and final are closed book exams.

  • The midterm will take place on Monday, October 26th from 12:00–15:00.
  • The final will take place on Monday, December 14th from 18:30–21:30.
Assignment Points
Assignments 30
Midterm examination 30
Final examination 40
Total 100

Weekly check-in

Every week, after you finish working through the content, I want to hear about what you learned and what questions you still have. To facilitate this, and to encourage engagement with the course content, you’ll need to write a small feedback in ZoneCours. This should be ~150 words.

You should answer the following three questions each week:

  • What was the most exciting thing you learned from the session? Why?
  • What was the muddiest thing from the session this week? What are you still wondering about?
  • Which activity did you find the most useful? What could have been skipped?

The weekly check-in is an occasion for you to ask for clarification, highlight areas or topics for which examples could be added, or list superfluous activities and content. I will read these before the next class, answer individually through the feedback form or at the beginning of class.

The submission module is on ZoneCours for convenience even if it carries no weight.

Student hours

Tuesday before class (14:30-15:15) or by appointment. My office, 4.850, is located next to the southern elevators in Lise-and-Giuseppe-Racanelli (Côte-Sainte-Catherine) building.

Please watch this video:

Intellectual integrity

Consult the school webpage for more details on HEC’s policy. The official policy lists the school rules regarding plagiarism and academic integrity (including use of artificial intelligence).

Student services

Students with special needs should feel free to approach me so we can best discuss accommodations. Do check out HEC Montréal’s disabled students and psychological support services.

Harassment and sexual violence

The Bureau du respect de la personne (BRP) is the unique access point for all members of the community subject to harassment or sexual violence. You can reach them at 514 343-7020 or by email at respect@hec.ca from Monday until Friday, from 8:30 until 4:30pm (in person meetings by appointment).

If you are in an emergency situation or fear for your safety, call emergency services at 911, followed by HEC Montréal security services at 514 340-6611.

Check the school official policy on these matters for more details.

Family policy

HEC has an official family policy.

References

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (3rd ed.). Chapman; Hall/CRC. https://doi.org/10.1201/b16018
Gelman, A., Vehtari, A., McElreath, R., Simpson, D., Margossian, C. C., Yao, Y., Kennedy, L., Gabry, J., Bürkner, P.-C., Modrák, M., & Barajas, V. L. (2026). Bayesian workflow. Chapman & Hall.
Held, L., & Bové, D. S. (2020). Likelihood and Bayesian inference: With applications in biology and medicine (2nd ed.). Springer Berlin. https://doi.org/10.1007/978-3-662-60792-3
Johnson, A. A., Ott, M. Q., & Dogucu, M. (2022). Bayes rules! An introduction to applied Bayesian modeling (1st ed.). Chapman; Hall/CRC. https://doi.org/10.1201/9780429288340
McElreath, R. (2020). Statistical rethinking: A Bayesian course with examples in R and STAN (2nd ed.). Chapman; Hall/CRC.
Villani, M. (2025). Bayesian learning: A gentle introduction. https://mattiasvillani.com/BayesianLearningBook/