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Module ST3453: Stochastic Models in Space and Time I
- Credit weighting (ECTS)
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5 credits
- Semester/term taught
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Michaelmas term 2014-15
- Contact Hours
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10 weeks, 3 lectures including tutorials per week
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- Lecturer
- STATS
- 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
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- 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
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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.