A random field is a stochastic process x(t) on Td, where T = R or Z and d >= 1 . When d= 1 and t designates time, x(t) is also known as a time series. Random field data occur when a physical quantity is measured at regular intervals of time and/or space, for example a digitised image can be considered as a realisation of a random field on Z2, where the physical measurements are of intensities of light.
There are two typical approaches to the statistical analysis of random field data. One is to fit a parametric model (ARMA or Markov) to describe the spatial/temporal dependence, the other is to estimate the distribution of power non-parametrically (kernel smoothing or using wavelets). The former lends itself to synthesis, prediction or interpolation while the latter can be used for model identification and estimation and is particularly useful for pattern recognition.
Further research directions include hidden Markov models and estimation of evolutionary spectra. More application orientated projects could be face/iris recognition and financial time series modelling.
Dr Jingsong Yuan, Tel: +44 (0)161 306 3695, E-mail: Jingsong.Yuan (@manchester.ac.uk)