Applied Probability Models for Decision Making

Course Coordinator: Dr Tony M T Chan, Grad Dip, MPhil (CUHK); PhD (CityU)

This is a higher-level course about the application of probability to modeling real-life situations. The emphasis in the course is on modeling practical situations and developing the properties of the models. Since this is a higher-level mathematics course, you will be expected to have fluency in mathematical manipulation. Some new mathematical techniques are introduced and taught in the course. MATH S350 is one of the compulsory higher-level courses for BSc and BSc (Hons) in Statistics and Decision Science programmes, and an optional course for BSc and BSc (Hons) in Mathematical Studies programme.

This course is also suitable for any learner who wishes to pursue further studies in more sophisticated probability models in order to enhance their career prospects in the areas of medical sciences, demographics, finance and engineering.

Advisory prerequisite(s)
You are advised to have already studied MATH S245/MATH S246/MATH S248/MATH S280.

Aims
This course aims to:

• Introduce the advanced probability theory and some advanced stochastic and deterministic models, and their application to solving problems of decision science;
• Enable students to understand the theory and methods for decision analysis under uncertainty, to appreciate the use of expert judgment and the value of information in decision-making, and to apply this information in industrial and financial areas;
• Teach students to set up probability models for real situations such as changing population sizes, queues, epidemics and events occurring in space, and the investigate the properties of these models using a variety of mathematical techniques.

Contents
The course covers the following topics:

• Random processes
• Patterns in space
• Branching processes
• Random walks
• Markov chains
• Birth processes
• Birth and death processes
• Queues
• Epidemics
• Population models
• Decision analysis
• Renewal models

Learning support
There will be 12 two-hour tutorials and four surgeries throughout the course.

Assessment
There are four assignments (from which the best three scores will be used to determine the final grade) and a final examination. Students are required to submit assignments via the Online Learning Environment (OLE).

Online requirement
This course is supported by the Online Learning Environment (OLE). You can find the latest course information from the OLE. Through the OLE, you can communicate electronically with your tutor and the Course Coordinator as well as other students. To access the OLE, students will need to have access to the Internet. The use of the OLE is required for the study of this course and you can use it to submit assignments.

Set book(s)
There are no set books for this course.

Student with disabilities or special educational needs
The audio and visual components of this course may cause difficulties for students with a hearing or visual impairment. You are encouraged to seek the advice from the Course Coordinator before enrolling in the course.