Module overview
Aims and Objectives
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- Understand properties of maximum likelihood estimators
- Evaluate different estimators using their theoretical properties;
- Derive generating functions and use them to determine distributions and moments
- Understand concepts of Bayesian inference
- Understand concept of a hypothesis test and confidence intervals and how to construct these with good properties
- Find distributions of functions of random variables, including distributions of maximum and minimum observations, and use these results to derive methods to simulate observations from standard distributions
Syllabus
Mgfs and Cgfs
Transformations of random variables (univariate, bivariate, sums and extremes, include derivation of t, F and Beta)
Point estimation (unbiased, MSE, consistency, sufficiency, MVUE, Rao-Blackwell)
Revision of ML
Asymptotics of ML
Hypothesis testing (Uniformly most powerful test & Neyman-Pearson lemma)
Confidence intervals
Bayesian inference
Learning and Teaching
Teaching and learning methods
Lectures, problem classes
| Type | Hours |
|---|---|
| Independent Study | 102 |
| Teaching | 48 |
| Total study time | 150 |
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Coursework | 30% |
| Exam | 70% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |