Course co-ordinator(s): Dr Seva Shneer (Edinburgh), Dr Fraser Daly (Edinburgh).
Aims:
To introduce stochastic processes used in stochastic and statistical modelling, and to provide an introduction to modern mathematical tools for studying such processes
Detailed Information
Course Description: Link to Official Course Descriptor.
Pre-requisites: none.
Location: Edinburgh.
Semester: 2.
Syllabus:
• Branching process
- Definition
- Survival vs extinction
- Moments for number of individuals in a generation
- Limiting results
- Branching random walks
• Approximations for sums of random variables
• Random Graph models
- Introduction and basic definitions of graphs and associated theory
- Definition of random graph models
- Basic properties of random graph models including Erdos-Reyni random graph, preferential attachment, configuration model
• Percolation and epidemic and data spread over a graph
Learning Outcomes: Subject Mastery
After studying this module, students should be able to:
• Understand the definition and basic properties of branching processes
• Calculate various statistics of interest for branching processes
• Understand the concept of a branching random walk
• Define various models of random graphs
• Apply certain approximation techniques for sums of random variables
• Calculate various statistics of interest for a range of random graph models
• Understand the concept of percolation and data/epidemic spread on a graph
Learning Outcomes: Personal Abilities
At the end of this course, students should be able to
• demonstrate self-initiative and the capacity for independent thought
• manage time and prioritize workloads
• present technical results clearly and coherently
Assessment Methods:
Assessment: Examination: (weighting – 80%) Coursework: (weighting – 20%)
Re-assessment: Examination: (weighting – 100%)
Re-assessment in next academic year
SCQF Level: 11.
Credits: 15.
Other Information
Help: If you have any problems or questions regarding the course, you are encouraged to contact the lecturer
VISION: further information and course materials are available on VISION