Overview
This course develops statistical decision theory as a framework for selecting actions under uncertainty. Students formalize decision problems using action spaces, states of nature, loss and utility functions, risk functions, and decision rules.
Topics include Bayes and minimax rules, admissibility, complete and sufficient statistics, unbiased and minimum-risk procedures, likelihood-based decisions, hypothesis testing, estimation, prediction, sequential decisions, stopping rules, sample-size considerations, and constrained decision analysis. Frequentist and Bayesian perspectives are compared through mathematical, computational, and applied work.
Applications include medical treatment selection, quality control, policy analysis, and business risk. Emphasis is placed on evaluating competing procedures, assessing sensitivity to model and utility assumptions, distinguishing statistical evidence from value judgments, considering ethical consequences, and communicating recommendations clearly to technical and nontechnical audiences.
Learning Outcomes
- Formalize real-world uncertainty problems using states of nature, action spaces, loss functions, utility functions, and decision rules.
- Calculate and interpret expected loss, risk functions, posterior risk, and related performance measures.
- Construct and evaluate Bayes, minimax, admissible, unbiased, and minimum-risk procedures.
- Apply complete and sufficient statistics to simplify statistical decision problems and justify procedure selection.
- Compare frequentist and Bayesian approaches to estimation, testing, prediction, and treatment or policy decisions.
- Evaluate likelihood-based and sequential decision procedures, including sample-size and stopping considerations.
- Assess the robustness of recommendations to alternative models, prior distributions, utility structures, and constraints.
- Synthesize computational and theoretical evidence to recommend transparent, ethically defensible actions.
- Communicate statistical decisions, assumptions, uncertainty, and sensitivity analyses to technical and nontechnical audiences.
Timetable
| Type | Length | Frequency | Period |
|---|---|---|---|
| Lecture | 2 hours | Weekly | All semester |
| Tutorial | 2 hours | Weekly | All semester |
| Lab | 2 hours | Fortnightly | All semester |
Assessment Schedule
| Type | Description | Weighting |
|---|---|---|
| Assignment | Decision-problem formulation assignment | 15.00% |
| Assignment | Computational decision analysis assignment | 15.00% |
| Quiz | Quizzes (4 × 5%) | 20.00% |
| Test | Practical test | 20.00% |
| Exam | Final examination | 30.00% |
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.