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Module ST3453: Stochastic Models in Space and Time I

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2014-15
Contact Hours
10 weeks, 3 lectures including tutorials per week
Learning Outcomes
On successful completion of this module, students will have ability to discuss and model simple versions of the following processes in times:
  • Markov chains, with particular emphasis on binary chains;
  • Counting processes in continuous time, with particular emphasis on Poisson processes;
  • Discrete and continuous time Gaussian processes;
  • Hidden Markov models, with particular emphasis on noisy observations of binary chains;
  • And to extend the application of Poisson and Gaussian processes to space;
Module Content
  • Examples by Monte Carlo simulation;
  • Binary Markov Chains in time, (revision of joint, marginal and conditional distributions; and application to missing or noisy observation);
  • Simple examples of more general Markov chains;
  • Poisson processes in continuous time, application to simple examples including (thinning; Inhomogeneous processes);
  • Gaussian processes in discrete time including (AR and MA processes used in forecasting; Noisy observations of GPs and HMMs);
  • Gaussian processes in continuous time, characterised by covariance functions;
  • Brief extension of GPs to 2D space.
Module Prerequisite
ST2351 and ST2352
Recommended Reading
Ross, S.M. Introduction to Probability Models, Academic Press. 8th edition 2003 519.2 M94*7;7th edition 519.2 M94*6;6th edition 2002 PL-403-442; 5th edition 1993 PL-224-947. In the 6th edition, Ch 1-4,6,10 are relevant.
Assessment Detail
This module will be examined jointly with ST3454 in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination.