MAS3931 : Markov Processes
- 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 2 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 |
| MAS2907 | Stochastic Processes |
| MAS2909 | Probability |
Pre Requisite Comment
N/A
Co-Requisite
Modules you need to take at the same time
| Code | Title |
|---|---|
| MAS3928 | Statistical Modelling |
Co Requisite Comment
N/A
Aims
To develop a knowledge and appreciation of Markov processes in continuous time and their
application to stochastic mathematical modelling.
The modelling of many biological and physical systems is often naturally done in continuous time.
Markov processes are the most important family of stochastic processes which evolve in
continuous time and have been widely used, with applications in areas such as epidemiology,
ecology, chemical reactions and statistical physics. We will encounter mathematical tools for
building and analysing stochastic processes in continuous time, and use them to consider some of
these applied examples.
Outline Of Syllabus
Review of Poisson processes and the exponential distribution. Markov processes on discrete state
spaces: transition probabilities, rate matrices, and the Kolmogorov equations. Stationary
distributions, reversibility and detailed balance. The case of finite state space. Birth-death models.
Dwell times and stochastic simulation algorithms. Multivariate Markov processes: models of
epidemics and predator-prey populations.
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Guided Independent Study | Assessment preparation and completion | 2 | 4:00 | 8:00 | Completion of in-course assessments. |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem classes |
| Guided Independent Study | Assessment preparation and completion | 1 | 2:00 | 2:00 | Unseen exam |
| Scheduled Learning And Teaching Activities | Practical | 5 | 1:00 | 5:00 | Computer practical's |
| Guided Independent Study | Independent study | 13 | 1:00 | 13:00 | Revision for unseen exam. |
| Guided Independent Study | Independent study | 2 | 1:30 | 3:00 | Review of coursework |
| Guided Independent Study | Independent study | 20 | 1:00 | 20:00 | Background reading on lectured content. |
| Guided Independent Study | Independent study | 22 | 1:00 | 22:00 | Preparation time for lectures. |
| Total | 100:00 |
Jointly Taught With
| Code | Title |
|---|---|
| MAS8617 | Markov Processes with advanced topics |
Teaching Rationale And Relationship
N/A
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 | 2 | A | 80 | 2 hour written exam, comprising a Section A and a Section B. |
Exam Pairings
| Module Code | Module Title | Semester | Comment |
|---|---|---|---|
| Markov Processes with advanced topics | 2 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 20 | Written exercises |
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 | 2 | 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.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way 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 coursework assignments allow the students to develop their problem-solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; the summative assessment has a secondary formative purpose as well as its primary summative purpose.
Note: the exam for MAS8717 is more challenging than the exam for MAS3931.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS3931's Timetable