Undergraduate

modules

Modules

MAS3909 : Markov Processes

Semesters
Semester 2 Credit Value: 10
ECTS Credits: 5.0

Aims

To develop a knowledge and appreciation of Markov processes in continuous time and their application to stochastic mathematical modelling

Module summary
The modelling of many biological and physical systems is often naturally done in continuous time. If we also wish to model the uncertainty inherent in the system, then we need a family of stochastic processes which evolve in continuous time. Markov processes are the most important such family and have been widely used. Applications include modelling outbreaks of infectious disease, complex biological networks and even exchange rates.

The first part of this course will develop the mathematical details behind Markov processes. We will illustrate how simple processes can help us understand complex dynamical systems. The second part of the course will consider more complex, real-world networks. R will be used to explore straightforward algorithms for simulating these systems.

Outline Of Syllabus

Review of Poisson processes and exponential distribution. Markov processes: Markov jump processes with infinite state space, Kolmogorov equations, birth-death models, predator-prey system, equilibrium probabilities. Diffusion processes. Stochastic simulation algorithms. Real-world examples: biochemical networks, susceptible-infective-removal models. Parameter estimation for the complete data likelihood.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Guided Independent StudyIndependent study122:0022:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study33:009:00Review of problem-solving exercises and group project
Guided Independent StudyIndependent study112:0012:00Preparation for group project
Guided Independent StudyIndependent study26:0012:00Preparation for problem-solving exercises
Total100:00
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. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A85N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem solving exercises
Prob solv exercises2M10Group project
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The problem solving exercises are expected to consist of two assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The exercises and the group project 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; these are thus formative as well as summative assessments.

Reading Lists

Timetable