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Details of Grant 

EPSRC Reference: EP/K021672/1
Title: Functional Object Data Analysis and its Applications
Principal Investigator: Aston, Professor Sir JAD
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Kings College London University of Oxford University of Toulouse III Paul Sabatier
Washington State University
Department: Statistics
Organisation: University of Warwick
Scheme: EPSRC Fellowship
Starts: 01 July 2013 Ends: 31 December 2013 Value (£): 836,309
EPSRC Research Topic Classifications:
Medical Imaging Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:
Related Grants:
Panel History:
Panel DatePanel NameOutcome
30 Jan 2013 EPSRC Mathematics Fellowships Interviews - January 2013 Announced
06 Dec 2012 Mathematics Prioritisation Panel Meeting December 2012 Announced
Summary on Grant Application Form
When linguists are trying to determine how different languages are related or neuroscientists wish to know how one part of the brain is associated with another, how to analyse data which is both complex and massive is a fundamental question. However, an area of Statistics, namely Functional Data Analysis, where the data is described as mathematical functions rather than numbers or vectors, has recently been shown to be very powerful in these situations.

This fellowship aims to take functional data analysis and advance it so that much more complex data can be investigated. This will require establishing a careful statistical framework for the analysis of such functions even in situations where the functions have strict relationships. By considering the underlying mathematical spaces which the functions lie in, it is possible to construct valid statistical procedures, which preserve these relationships, such as the functions needing to be positive definite or the functions needing to be related by a graph or network.

As an example, comparison between different languages (for example, how is French quantitatively different from Italian) can be carried out in the framework of functional data but not without considering specifically how the data should be analysed to take into account its particular properties. For example in trying to find a path from one language to another, it would be sensible to try to only go via other feasible acoustic sounds. This turns out to be mathematically related to shape analysis, a simple example of which might be how to describe going from London to Sydney. The shortest path is through the centre of the Earth, but this is not sensible, so you have to go round the world. Establishing links between shape analysis and functional data is a major aim of this fellowship.

In addition, most brain analysis currently splits the brain up into lots of elements know as voxels, and then analyses these voxels one by one. However, the brain is really one object (or complex 3-D object) which should be analysed together. This is another example of functional data and the methods developed in this fellowship will enable the analysis of the brain as a single object. This will be done by examining the types of dependence between observations in brain imaging data, and using these to build such an object. Of particular interest will be the analysis of brain connections resulting from particular tasks which will require a mixture of functional data analysis and graphical or network analysis. However, before this can be done and the resulting insights into the brain found, the statistical methods required to do this need to be developed.

Key Findings
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Potential use in non-academic contexts
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Further Information:  
Organisation Website: http://www.warwick.ac.uk