|Module Name||Stochastic Models in Space and Time II|
|ECTS Weighting||5 ECTS|
|Semester taught||Semester 2|
|Module Coordinator/s||Dr. Jason Wyse|
Module Learning Outcomes
On successful completion of this module, students will be able to:
LO1. Describe and characterise auto-covariance structures in space and time
LO2. Formulate a model for spatially or temporally correlated data using a hidden (latent) Markov model
LO3. Fit a hidden Markov model in discrete time using the expectation maximization algorithm
LO4. Define and simulate realisations from an auto-logistic model and appreciate equivalence to the Ising model
LO5. Describe Gaussian processes and how they can be used in spatial modelling applications.
This module introduces different statistical modelling used for analysing stochastic processes defined in the spatial and/or time domains. These have many applications (e.g. engineering, finance, genetics).
Topics covered include:
- Hidden Markov models and applications
- Besag’s auto-models and connections with the Ising model from physics
- Gaussian Markov Random Field models and their use in epidemiological applications
- Gaussian processes and discussion of key topics such as the covariance function
Teaching and learning Methods
Lectures and tutorials. Lectures include some programming demonstrations.
|Assessment Component||Brief Description||Learning Outcomes Addressed||% of total||Week set||Week Due|
|Examination||Take home exam||LO1.-LO5.||90%||TBC|||
|Assignments||Four assignments throughout semester||LO1.-LO5.||10%||TBC|||
Reassessment of this module will be through an exam worth 100%.
Contact Hours and Indicative Student Workload
|Contact Hours (scheduled hours per student over full module), broken down by:||33 hours|
|Tutorial or seminar||4 hours|
|Independent study (outside scheduled contact hours), broken down by:||82 hours|
|Preparation for classes and review of material (including preparation for examination, if applicable||42 hours|
|completion of assessments (including examination, if applicable)||40 hours|
|Total Hours||115 hours|
Recommended Reading List
Students are not required to buy a specific text for this module and notes provided should suffice to study for the module. However, the texts below will complement the material delivered in the module.
“Pattern Recognition and Machine Learning” by C. M. Bishop, published by Springer
“Spatial Statistics” by B. Ripley, published by Wiley
“Gaussian Markov Random Fields: Theory and Application” by H. Rue and L. Held, published by CRC press
Prerequisite modules: STU23501, STU22005, STU34503
Other/alternative non-module prerequisites: