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.