MAS3927 : Mathematical Statistics
- Offered for Year: 2026/27
- Available for Study Abroad and Exchange students, subject to School approval at module registration
- Module Leader(s): Mr Axel Finke
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
| Semester 1 Credit Value: | 10 |
| ECTS Credits: | 5.0 |
| European Credit Transfer System | |
Pre-requisite
Modules you must have done previously to study this module
| Code | Title |
|---|---|
| MAS2901 | Statistical Inference |
| MAS2909 | Probability |
Pre Requisite Comment
N/A
Co-Requisite
Modules you need to take at the same time
Co Requisite Comment
N/A
Aims
This module aims to provide a mathematically rigorous treatment of the fundamental principles of
statistical inference, building upon the foundations of probability and statistics encountered
previously. Students will learn how core inferential procedures—estimation, hypothesis testing, and
interval estimation—arise from general statistical models, and will explore their theoretical properties
and asymptotic behaviour. The module emphasises the logical structure and proofs underlying
statistical methods, preparing students for advanced study or research in statistics, econometrics,
data science, or related mathematical fields.
Outline Of Syllabus
Statistical models: sufficiency, completeness, exponential families, chi-square, t-distributions and Fdistributions. Unbiased estimation: Rao–Blackwell theorem, uniformly minimum variance unbiased
estimators, Lehmann–Scheffé theorem, Cramér–Rao lower bound, Gauss-Markov theorem.
Hypothesis testing: Neyman–Pearson lemma, uniformly most powerful tests, likelihood-ratio test.
Confidence sets. Large sample theory: asymptotics of estimators, and related confidence sets and
hypothesis tests. Covariance estimation.
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in-course assessment |
| Guided Independent Study | Independent study | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
| Total | 100:00 |
Teaching Rationale And Relationship
The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.
Assessment Methods
The format of resits will be determined by the Board of Examiners
Exams
| Description | Length | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination | 120 | 1 | A | 80 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 1 | M | 20 | Problem-solving exercises assessment, in course assessment. |
Formative Assessments
Formative Assessment is an assessment which develops your skills in being assessed, allows for you to receive feedback, and prepares you for being assessed. However, it does not count to your final mark.
| Description | Semester | When Set | Comment |
|---|---|---|---|
| Prob solv exercises | 1 | M | Problem-solving exercises. |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.
Exam problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
The in course assessment allows students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; the assessment therefore has a secondary formative purpose as well as a primary summative purpose.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS3927's Timetable