STU34504 – Stochastic Models in Space and Time II
Source: https://teaching.scss.tcd.ie/module/stu34504-stochastic-models-in-space-and-time-ii-2/ Parent: https://www.maths.tcd.ie/undergraduate/modules/minor-stats.php
Not offered in 2023/24
| Module Code | STU34504 |
| Module Name | Stochastic Models in Space and Time II |
| ECTS Weighting [1] | ECTS |
| Semester Taught | Semester 2 |
| Module Coordinator/s | Jason Wyse |
Module Learning Outcomes
On successful completion of this module, students will be able to:
-
Describe and characterise auto-covariance structures in space and time
-
Formulate a model for spatially or temporally correlated data using a hidden (latent) Markov model
-
Fit a hidden Markov model in discrete time using the expectation maximization algorithm
-
Define and simulate realisations from an auto-logistic model and appreciate equivalence to the Ising model
-
Describe Gaussian processes and how they can be used in spatial modelling applications
Module Content
Specific topics addressed in this module include:
- Motivating stochastic models in space
- Autocovariance and autocorrelation functions
- Hidden Markov models
- Expectation-Maximization algorithm to estimate Hidden Markov Models
- Binary Markov Random Fields on lattices
- Gaussian Markov Random Fields with applications
- Gaussian Processes and kriging
This course introduces different statistical models used for analysing stochastic processes defined in the spatial and/or time domains. These have many applications (e.g. engineering, finance, genetics). Topics 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 and computational considerations when using spatial statistical models. Concepts and ideas will be demonstrated through simulation and model fitting using the statistical computing language R. Code libraries tailored to the module are provided to accompany lecture material.
Teaching and Learning Methods
Lectures including code demonstrations and tutorials.
Assessment Details
2 hour real-time examination and homework assignments.
| Assessment Component | Brief Description | Learning Outcomes Addressed | % of Total | Week Set | Week Due |
| Examination | 2 hour written examination | LO1, LO2, LO3, LO4, LO5 | 90% | N/A | N/A |
| Assignments | Four assignments throughout semester | LO1, LO2, LO3, LO4, LO5 | 10% | 2,4,7,9 | 3,5,8,10 |
Reassessment Details
Written examination (2 hours, 100%)
Contact Hours and Indicative Student Workload
| Contact Hours (scheduled hours per student over full module), broken down by: | 33 hours |
| Lecture | 29 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. The texts below should complement the material delivered in the module.
“Pattern Recognition and Machine Learning” by Christopher M. Bishop, published by Springer
“Spatial Statistics” by Brian Ripley, published by Wiley
“Gaussian Markov Random Fields: Theory and Application” by Havard Rue and Leonard Held, published by CRC press
Module Pre-requisites
Prerequisite modules
Mathematics students: STU23501, STU34503
MSISS students: STU11002, STU22004, STU34503
Other/alternative non-module prerequisites: Solid knowledge in mathematics and statistics required e.g. on Linear algebra, Integration and differentiation, expectation operator
Module Co-requisites
N/A