Undergraduate Course: Theory of Statistical Inference (MATH10028)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | In this course we will develop mathematical aspects of statistical inference. The theory covered provides a greater understanding of the fundamental properties of popular statistical techniques and provides a framework for deriving procedures in more complex situations. |
| Course description |
Topics to be covered include:
1. Parametric families and likelihood.
2. Statistics, Sufficiency and Minimal Sufficiency.
3. Estimation, Unbiasedness, Efficiency, MVUE, Rao--Blackwell Theorem, Cramer--Rao Lower Bound.
4. Hypothesis testing, Neyman--Pearson Lemma.
5. Confidence Intervals, Pivots
6. Decision theory and admissibility of estimators.
7. Shrinkage/James Stein estimators.
8. Selected topics in modern statistics.
|
Information for Visiting Students
| Pre-requisites | This is a Year 4, Honours level course. Visiting students are expected to have an academic profile equivalent to the first three years of the BSc (Hons) Mathematics programme (UTMATHB). Students should have passed courses equivalent to Several Variable Calculus and Differential Equations (MATH08063); Fundamentals of Pure Mathematics (MATH08064); and Statistical Methodology (MATH10095). |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2025/26, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
|
| Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 0%, Examination 100% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Minutes |
|
| Main Exam Diet S1 (December) | Theory of Statistical Inference (MATH10028) | 120 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Write down formal definitions of statistical properties
- State and prove standard theoretical results in statistical inference
- Construct estimators, hypothesis tests and confidence intervals which satisfy desirable statistical properties
- Apply statistical theorems in examples to ascertain the properties of particular estimators, hypothesis tests and confidence intervals
|
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | TSI |
Contacts
| Course organiser | Dr Timothy Cannings
Tel:
Email: Timothy.Cannings@ed.ac.uk |
Course secretary | Miss Kirstie Paterson
Tel:
Email: Kirstie.Paterson@ed.ac.uk |
|
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