MA22038: Probabilistic modelling
[Page last updated: 03 June 2024]
| Academic Year: | 2024/25 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 5 [equivalent to 10 CATS credits] |
| Notional Study Hours: | 100 |
| Level: | Intermediate (FHEQ level 5) |
| Period: |
- Semester 1
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| Assessment Summary: | EXCB 100% |
| Assessment Detail: |
- Closed-book written examination (EXCB 100%)
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| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before taking this module you must ( take MA12004 AND take MA12003 ) OR ( take MA12011 AND take MA12008 ) OR take MA12013
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| Learning Outcomes: |
On completing the unit, you will be able to:
- Find transition probabilities, hitting probabilities, expected hitting times, and invariant distributions of discrete time Markov chains;
- Classify the states of a Markov chain;
- Calculate the limiting behaviour of Markov chains;
- Set up simple Markov chain models.
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| Synopsis: | This unit will introduce you to mathematical modelling using stochastic processes. You will explore Markov chains and learn to analyse their long-term behaviour. You will cover applications of these models in a wide range of areas, such as for example, biological processes, phenomena in economics, but also card shuffling.
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| Content: | Discrete-time Markov property; transition matrix, n-step transition probabilities; basic examples, including random walk; hitting probabilities and expected hitting times; classification of states; convergence to equilibrium and ergodic theorem; symmetrizability. Optional: Numerical exploration of Monte-Carlo method. Examples will be chosen, among others, from physical and biological processes, economics, telecommunications.
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| Course availability: |
MA22038 is Optional on the following courses:
Department of Computer Science
- USCM-AFB32 : BSc(Hons) Computer Science and Mathematics (Year 2)
- USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with professional placement (Year 2)
- USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with study abroad (Year 2)
Department of Economics
- UHES-AFB12 : BSc(Hons) Economics and Mathematics (Year 2)
- UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement (Year 2)
- UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement and study abroad (Year 2)
- UHES-AKB12 : BSc(Hons) Economics and Mathematics with study abroad (Year 2)
Department of Mathematical Sciences
- USMA-AFB30 : BSc(Hons) Mathematics (Year 2)
- USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 2)
- USMA-AKB32 : BSc(Hons) Mathematics and Statistics with professional placement (Year 2)
- USMA-AKB32 : BSc(Hons) Mathematics and Statistics with study abroad (Year 2)
- USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 2)
- USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with professional placement (Year 2)
- USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with study abroad (Year 2)
- USMA-AKB30 : BSc(Hons) Mathematics with professional placement (Year 2)
- USMA-AKB30 : BSc(Hons) Mathematics with study abroad (Year 2)
- USMA-AFM30 : MMath(Hons) Mathematics (Year 2)
- USMA-AKM30 : MMath(Hons) Mathematics with professional placement (Year 2)
- USMA-AKM31 : MMath(Hons) Mathematics with study abroad (Year 2)
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Notes: - This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
- Courses and units are subject to change in accordance with normal University procedures.
- Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
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