MAS275 Probability Modelling
|Semester 2, 2013/14||10 Credits|
|Lecturer:||Dr Jonathan Jordan||Home page||Timetable||Reading List|
The course introduces a number of general models for processes where the state of a system is fluctuating randomly over time. Examples might be the length of a queue, the size of a reproducing population, or the quantity of water in a reservoir. The aim is to familiarize students with an important area of probability modelling.
Prerequisites: MAS201 (Linear Mathematics for Applications); MAS202 (Advanced Calculus); MAS205 (Statistics Core)
The following modules have this module as a prerequisite:
|MAS352||Stochastic Processes and Finance|
|MAS452||Stochastic Processes and Finance|
- Discrete time renewal processes
- Discrete time Markov chains
- Random point processes in time and space
- To introduce and study a number of general models for processes where the state of a system is fluctuating over a period of time according to some random mechanism.
- To illustrate the above models by example and by simulation.
- To familiarise students with an important area of probability modelling.
- model a range of situations by writing down transition matrices for suitable Markov chains.
- calculate and interpret equilibrium probabilities and distributions of Markov chains.
- calculate and interpret absorption probabilities and expected times to absorption in Markov chains.
- understand the special properties of the simple Poisson process, perform calculations with them and interpret the results.
- understand the spatial and inhomogeneous extensions of the Poisson process, and apply them as models of real phenomena.
21 lectures, 5 tutorials
One formal 2 hour closed book examination.
- Discrete time renewal processes: Definition, generating functions, the renewal theorem, delayed renewal processes.
- Discrete time Markov chains: Transition probabilities, classification of states, equilibrium and absorption probabilities. Examples: gambler's ruin, inventory models, dam models, diffusion of particles.
- Random point processes in time and space: Poisson process: superposition, censoring, conditioning on number of events in an interval. Inhomogeneous, compound and spatial generalisations.
|C||E. Parzen||Stochastic Processes||519.23 (P)||Blackwells||Amazon|
|C||G.R. Grimmett, D.R.Stirzaker||Probability and Random Processes||519.2 (G)||Blackwells||Amazon|
|C||S.M. Ross||Introduction to Probability Models||519.2 (R)||Blackwells||Amazon|
|C||W. Feller||An Introduction to Probability Theory and its Applications||519.2 (F)||Blackwells||Amazon|
(A = essential, B = recommended, C = background.)
Most books on reading lists should also be available from the Blackwells shop on Mappin Street.
|Mon||11:00 - 11:50||lecture||Arts Tower Lecture Theatre 3|
|Tue||12:00 - 12:50||tutorial||(group 81)||(even weeks)||K14 Hicks Building|
|Wed||11:00 - 11:50||lecture||Psychology Lecture Theatre G30|
|Wed||12:00 - 12:50||tutorial||(group 82)||(even weeks)||Hicks Lecture Theatre 4|
|Thu||12:00 - 12:50||tutorial||(group 83)||(even weeks)||Hicks Lecture Theatre 10|