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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 Activities
Lecture
20
1:00
20:00
Formal Lectures – Present in Person
Scheduled Learning And Teaching Activities
Lecture
2
1:00
2:00
Revision Lectures – Present in Person
Scheduled Learning And Teaching Activities
Lecture
4
1:00
4:00
Problem Classes – Synchronous On-Line
Guided Independent Study
Assessment preparation and completion
15
1:00
15:00
Completion of in course assessments
Scheduled Learning And Teaching Activities
Practical
4
1:00
4:00
Computer Practicals – Present in Person
Scheduled Learning And Teaching Activities
Drop-in/surgery
4
1:00
4:00
Drop-in – Synchronous On-Line
Guided Independent Study
Independent study
51
1:00
51:00
Preparation time for lectures, background reading, coursework review
Total
100:00
Jointly Taught With
Code
Title
MAS8909
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.
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
1
A
80
N/A
Exam Pairings
Module Code
Module Title
Semester
Comment
MAS8909
Markov Processes
1
N/A
Other Assessment
Description
Semester
When Set
Percentage
Comment
Prob solv exercises
1
M
10
Coursework assignment
Prob solv exercises
1
M
10
Coursework 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.
