If you are interested in any of the projects below (or other general projects in areas which I am interested in), please contact me. 

Project 1: Joint Project with ONS on Time Series Analysis (part of the ESRC DTC)

Supervisor: John Aston 

For more information see this PDF.

Project 2: Spatial-Temporal Covariance Functions For Neuroimaging Data Sets

Supervisor: John Aston

Functional brain imaging requires the analysis of massive four dimensional data sets. In particular, there is interest in designing covariance functions to account for the space-time correlations. One possible methodology is to use techniques from functional data analysis to design these covariance functions. Of interest will be to view the images themselves as data points, and as such to look at the effect of smoothness assumptions on the design of these covariance functions, particularly as these will be very high dimensional functions. The developed techniques can then be compared and contrasted with standard methods from spatial and spatial-temporal analysis. The techniques would also have application in other areas such as computer vision.

Project 3: Sequential Monte Carlo Interpolation

Supervisors: Adam Johansen and John Aston

Often when collecting data over time, both the dynamics that the observed data undergoes and data at times that were not observed in the sequence are of interest. This can be of particular importance when different data sets are collected at different times and cross comparison is required. Sequential Monte Carlo methods either explicitly or implicitly specify certain dynamics, and so as part of the inference, samples of the path can also be obtained. This project would focus on understanding the methodology required to obtain path samples for different spaces (vector spaces or even function spaces) for certain computational costs and using these to interpolate between the underlying data. This will be of particular interest in applications such as speech processing where speech patterns could be interpolated to produce additional realistic speech, or in brain imaging where brain morphologies changes caused by aging could be analysed and compared across individuals.

Information about PhDs in the Department of Statisitics