Undergraduate Course: Stochastic Modelling (MATH10007)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 3 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | Specialist Mathematics & Statistics (Honours) |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | Core course for Honours Degrees involving Statistics; optional course for Honours degrees involving Mathematics.
Syllabus summary: Probability review: Conditional probability, basic definition of stochastic processes. Discrete-time Markov chains: Modelling of real life systems as Markov chains, transient behaviour, limiting behaviour and classification of states, first passage and recurrence times, absorption problems, ergodic theorems, Markov chains with costs and rewards, reversibility. Poisson processes: Exponential distribution, counting processes, alternative definitions of Poisson processes, splitting, superposition and uniform order statistics properties, non-homogeneous Poisson processes. Continuous-time Markov chains: transient behaviour, limiting behaviour and classification of states in continuous time, ergodicity, basic queueing models. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
|
| Delivery period: 2014/15 Semester 2, Available to all students (SV1)
|
Learn enabled: Yes |
Quota: None |
|
Web Timetable |
Web Timetable |
| Course Start Date |
12/01/2015 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
|
| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | Stochastic Modelling (MATH10007) | 2:00 | |
Summary of Intended Learning Outcomes
1. Basic understanding of stochastic processes and their characterization
2. Ability to analyze the transient behaviour of Markov chains
3. Ability to classify states of a Markov chain
4. Understanding stationary and limiting behaviour and deriving these probability distributions
5. Ability to calculate the finite dimensional distributions of Poisson processes
6. Appreciating the range of applications, together with a facility to model appropriate problems in terms of a stochastic process
|
Assessment Information
| Coursework 5%, Examination 95% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Markov Chains in discrete time: classification of states, first passage and recurrence times, absorption problems, stationary and limiting distributions.
Markov Processes in continuous time: Poisson processes, birth-death processes.
The Q matrix, forward and backward differential equations, imbedded Markov Chain, stationary distribution. |
| Transferable skills |
Not entered |
| Reading list |
http://www.readinglists.co.uk |
| Study Abroad |
Not Applicable. |
| Study Pattern |
See 'Breakdown of Learning and Teaching activities' above. |
| Keywords | SMo |
Contacts
| Course organiser | Dr Tibor Antal
Tel: (0131 6)51 7672
Email: Tibor.Antal@ed.ac.uk |
Course secretary | Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk |
|
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