MAS8617 : Markov Processes with advanced topics
- Offered for Year: 2026/27
- 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 | |
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. Additional advanced topics such as inference of model
parameters and continuous-time hidden Markov models will be considered
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| 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 | 6 | 1:00 | 6:00 | Background reading on lecture content |
| Guided Independent Study | Assessment preparation and completion | 2 | 4:00 | 8:00 | Completion of in-course assessments. |
| Guided Independent Study | Assessment preparation and completion | 1 | 2:00 | 2:00 | Unseen exam |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Guided Independent Study | Directed research and reading | 15 | 1:00 | 15:00 | Directed reading of advanced topic(s) |
| Scheduled Learning And Teaching Activities | Practical | 4 | 1:00 | 4:00 | Computer Practical |
| Guided Independent Study | Independent study | 2 | 1:30 | 3:00 | review of coursework. |
| Guided Independent Study | Independent study | 22 | 1:00 | 22:00 | Preparation time for lectures |
| Guided Independent Study | Independent study | 13 | 1:00 | 13:00 | Revision for unseen exam. |
| Total | 100:00 |
Jointly Taught With
| Code | Title |
|---|---|
| MAS3931 | Markov Processes |
Teaching Rationale And Relationship
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. Practical classes are used to help the
students’ practical ability to apply the methods to real data. In addition, directed research and
reading of an advanced topic is used to develop the students’ ability to learn independently.
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
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 | 2 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 20 | Coursework 2. Up to 6 page typeset report based upon a set assignment comprising open-ended questions. |
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 | Coursework 1. 40 minute class test, conducted during one of the timetabled one hour lecture slots. |
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 MAS8617 is more challenging than the exam for MAS3931.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS8617's Timetable