STU34504 – Stochastic Models in Space and Time II

Module CodeSTU34504
Module NameStochastic Models in Space and Time II
ECTS Weighting[1]5 ECTS
Semester taughtSemester 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.

Module Content

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 Details

Assessment ComponentBrief DescriptionLearning Outcomes Addressed% of totalWeek setWeek Due
ExaminationTake home examLO1.-LO5.90%TBC
AssignmentsFour assignments throughout semesterLO1.-LO5.10%TBC

Reassessment Details

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
Lectures29 hours
Tutorial or seminar4 hours
Independent study (outside scheduled contact hours), broken down by:82 hours
Preparation for classes and review of material (including preparation for examination, if applicable42 hours
completion of assessments (including examination, if applicable)40 hours
Total Hours115 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

Module Pre-requisites

Prerequisite modules: STU23501, STU22005, STU34503

Other/alternative non-module prerequisites:

Module Co-requisites


Module Website