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., OpenBugs, 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 three 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.
  • 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

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

The midterm and final are closed book exams. Any reference should be adequately cited.

There will be weekly exercises, which we will discuss at the beginning of the next class.

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 and quizzes 30
Midterm examination (30 pts) 30
Final examination (40 pts) 40
Total 100

Student hours

Tuesday before class or by appointment. My office, 4.850, is located next to the southern elevators in Côte-Sainte-Catherine building.

Please watch this video:

Intellectual integrity

The official policy lists the school rules regarding plagiarism and academic integrity.

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 Center for Harassment Intervention (BIMH) 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 harcelement@hec.ca from Monday until Friday, from 8:30 until 4:30pm.

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 now has an official family policy, but the following guidelines reflect my own beliefs and commitments towards parent students1

  1. Babies are welcome in class as often as necessary for support feeding relationship.
  2. You are welcome to bring your child to class in order to cover unforeseeable gaps in childcare.
  3. If you come with babies or toddler, I ask that you sit close to the door so that, in case your little one needs special attention and is disrupting the learning of other students, you may step outside of class until their needs are met. Seats close to the door are reserved for parents attending class with their child.

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/

Footnotes

  1. Shamelessly stolen/adapted from similar policy by Drs. Melissa Cheney, Guy Grossman and Rohan Alexander↩︎