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

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

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.