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Module

MAS8909 : Markov Processes

  • Offered for Year: 2021/22
  • Module Leader(s): Dr Andrew Golightly
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 1 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 ActivitiesLecture201:0020:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture41:004:00Problem Classes – Synchronous On-Line
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesPractical41:004:00Computer Practicals – Present in Person
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Drop-in – Synchronous On-Line
Guided Independent StudyIndependent study511:0051:00Preparation time for lectures, background reading, coursework review
Total100:00
Jointly Taught With
Code Title
MAS3909Markov 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.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A80N/A
Exam Pairings
Module Code Module Title Semester Comment
MAS3909Markov Processes2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Coursework assignment
Prob solv exercises1M10Coursework assignment
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. 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; these assessments have a secondary formative purpose as well as their primary summative purpose.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.

Reading Lists

Timetable