Overview
This course develops the mathematical foundations, computational methods, and applied practice of Bayesian statistical inference. Topics include probability and conditional probability, Bayes' theorem, likelihoods, prior and posterior distributions, conjugate models, posterior summaries, credible intervals, posterior predictive distributions, hypothesis assessment, hierarchical and multilevel models, model comparison, prior sensitivity, and decision-theoretic reasoning.
Students translate substantive questions into Bayesian models, select and justify informative or weakly informative priors, implement Monte Carlo and Markov chain Monte Carlo methods, and assess convergence and computational diagnostics. Practical work uses statistical software and probabilistic programming to analyse real datasets, evaluate model adequacy, communicate uncertainty accurately, and produce reproducible analyses. Emphasis is placed on mathematical reasoning, model criticism, ethical use of prior information, and distinction between credible intervals and frequentist confidence intervals.
Learning Outcomes
- Derive Bayesian posterior distributions from probability models, likelihoods, and prior specifications.
- Evaluate conjugate and nonconjugate Bayesian models for substantive and statistical appropriateness.
- Implement Monte Carlo simulation, importance sampling, Gibbs sampling, Metropolis-Hastings, and related computational methods.
- Diagnose convergence, mixing, effective sample size, and other computational properties of Markov chain Monte Carlo output.
- Construct and justify informative or weakly informative priors using substantive knowledge and sensitivity analysis.
- Compare hierarchical, multilevel, and competing statistical models using posterior and predictive criteria.
- Critique Bayesian models through posterior predictive checks, residual analysis, and assessment of prior and likelihood assumptions.
- Interpret posterior, predictive, and decision-theoretic results while distinguishing credible intervals from frequentist confidence intervals.
- Communicate Bayesian analyses with reproducible code, transparent assumptions, appropriate visualizations, and ethically responsible conclusions.
Timetable
| Type | Length | Frequency | Period |
|---|---|---|---|
| Lecture | 2 hours | Weekly | All semester |
| Lab | 2 hours | Weekly | All semester |
| Tutorial | 1 hour | Fortnightly | All semester |
Assessment Schedule
| Type | Description | Weighting |
|---|---|---|
| Assignment | Weekly problem sets (10 × 2%) | 20.00% |
| Assignment | Computational modelling assignment | 15.00% |
| Test | Mid-semester test | 20.00% |
| Deliverable | Reproducible Bayesian analysis project | 25.00% |
| Exam | Final examination | 20.00% |
Prerequisites
Teaching Staff & Programs
This course is delivered jointly by faculty from the participating programs listed below. In line with the Douchewater Way, the University of Sexology tailors core instruction directly to each cohort's specific discipline — adapting curriculum to program needs rather than forcing students into a one-size-fits-all model. Learn more about our approach at The Douchewater Way.