Module manager: Dr Jochen Voss
Email: J.Voss@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2026/27
MATH2701 Statistical Methods or equivalent
| MATH2701 | Statistical Methods |
| MATH3723 | Statistical Theory |
| MATH5741M | Statistical Theory and Methods |
MATH3723 Statistical Theory
This module is not approved as an Elective
From introductory statistics, you know how to calculate sample mean and variance, construct confidence intervals and test hypotheses in the normal model. This module focuses on the pivotal case with data in the form of independent samples and gives a general unified theory of statistical procedures such as parameter estimation and hypotheses testing, highlighting optimality and large-sample properties. The module also introduces a modern Bayesian approach in statistics, making comparisons with classical inference.
Through a combination of theory and example-based practice, the module will allow students to solidify and deepen their understanding of basic statistical techniques by appreciating a general unified theory of parameter estimation and hypotheses testing with a view on optimality and large-sample properties. A modern Bayesian approach to statistical problems will also be introduced and developed in parallel with classical statistical inference.
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject: 1. Understand the role of bias and mean squared error in parameter estimation and be able to calculate them in closed form or asymptotically. 2. Understand the concept of sufficiency and its use in constructing improved estimators via the Rao–Blackwell theorem. 3. Understand the Cramér–Rao inequality and the concept of Fisher’s information, including efficiency of estimators. 4. Understand large-sample properties of maximum likelihood estimators. 5. Understand the setting and main concepts of statistical hypothesis testing, including critical region and types of error. 6. Understand the power concept; apply the Neyman-Pearson lemma to simple hypotheses. 7. Understand the Bayesian approach to inference: prior and posterior distributions, Bayesian estimation and credible intervals. 11. Use a statistical package R with real or simulated data to fit parametric models and to write a report presenting and interpreting the results.
Main topics to be covered include: 1. Parameter estimation: bias, mean squared error, consistency. 2. Sufficiency: factorisation criterion, Rao–Blackwell theorem. 3. Fisher’s information, Cramér–Rao inequality. Vector case, Fisher’s information matrix. 4. Maximum likelihood and method of moments: examples; large-sample properties of maximum likelihood estimators. 5.Hypothesis testing: Neyman-Pearson lemma. 6. Confidence intervals. 7. Bayesian statistics: prior and posterior distributions. 8. Credible intervals. 9. Revision of standard tests. Additional topics that build on these may be covered as time allows. Further details of possible topics will be delivered closer to the time that the module runs.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Supervision | 0 | 0 | 0 |
| Lectures | 28 | 1 | 28 |
| Seminars | 5 | 1 | 5 |
| Practicals | 1 | 2 | 2 |
| Independent online learning hours | 7 | ||
| Private study hours | 108 | ||
| Total Contact hours | 35 | ||
| Total hours (100hr per 10 credits) | 150 | ||
Students receive formative feedback through regular exercises and practical work during the semester. This feedback does not contribute to the module mark.
Check the module area in Minerva for your reading list
Last updated: 14/10/2026
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