MAS3909 : Markov Processes
- Offered for Year: 2017/18
- Module Leader(s): Dr Colin Gillespie
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
|Semester 2 Credit Value:||10|
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. 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.
|Scheduled Learning And Teaching Activities||Lecture||3||1:00||3:00||Problem classes|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||25||1:00||25:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||1||13:00||13:00||Revision for unseen exam|
|Guided Independent Study||Assessment preparation and completion||1||2:00||2:00||Unseen exam|
|Guided Independent Study||Independent study||1||22:00||22:00||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||3||3:00||9:00||Review of problem-solving exercises and group project|
|Guided Independent Study||Independent study||1||12:00||12:00||Preparation for group project|
|Guided Independent Study||Independent study||2||6:00||12:00||Preparation for problem-solving exercises|
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.
The format of resits will be determined by the Board of Examiners
|Prob solv exercises||2||M||5||Problem solving exercises|
|Prob solv exercises||2||M||10||Group 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 List Website : rlo.ncl.ac.uk