PhD Studentship in Statistics at the Open University


Applications are invited for a full-time PhD studentship in Statistics commencing 1 October, 2012. The studentship will include University fees and a grant to cover living expenses. 

The studentship will be based at the Open University’s central campus in Milton Keynes, where there is a thriving postgraduate student  community. The Statistics Group at the Open University provides a lively and stimulating environment for Statistics research with active researchers working in a variety of fields of statistics. For more information about the Statistics Group see http://statistics.open.ac.uk/. 

Two possible Statistics projects are available:

Title: Sparse linear discrimination with more variables than observations
Supervisor: Dr Nickolay Trendafilov

Title: Better Beta distributions
Supervisor: Prof Chris Jones

Full details of each project can be found below.

Applicants should have a first or upper second class honours degree and, preferably, a recognized postgraduate qualification containing a substantial element of Statistics. Applications from all nationalities are welcome.

Informal enquiries may be made to Heather Whitaker (email: [log in to unmask]).


Application process

The Open University’s Research Degrees Prospectus and application form, can be found at http://www.open.ac.uk/research/research-degrees/. 
When applying for the studentship please include:

a)	a completed application form (note that where the standard application form asks for a research proposal, simply indicate which (one or more) of the advertised projects you are interested in),

and

b)	a covering letter explaining why you want to do a PhD and why you are interested in one or other (or both) projects.

Closing date for applications: Friday, 17 February, 2012. 



Project details

Project: Sparse linear discrimination with more variables than observations
Supervisor: Dr Nickolay Trendafilov

Many important modern applications require analyzing data with more variables than observations. In such situation the classical Fisher’s linear discriminant analysis (LDA) does not possess solution because the within-group scatter matrix is singular. Moreover, the number of the variables is usually huge and the classical type of solutions (discriminant functions) are difficult to interpret as they involve all available variables. 

The aim is to develop fast and reliable algorithms for sparse LDA of data with more variables than observation. The resulting discriminant functions will depend on very few original variables, which will facilitate their interpretation. 

Application will be sought in areas as shape, image, handwritten character recognition and classification, and analysis of gene expression (microarray) data, where most recent developments are oriented to and tested.


Project: Better Beta distributions 
Supervisor: Prof Chris Jones

The standard (two-parameter) distribution for random variables on a known interval is the beta distribution; it has roles as a model for data and as a prior distribution for probabilities. But can one do better? Lots of alternatives already exist. Which, at each level of complexity (number of parameters), are best? Can one parameterise some distribution(s) to enhance interpretability and estimability? How do distributions defined directly compare with distributions derived by transformation from other supports? How best should these distributions be deployed in regression contexts? Which are best for use with the probability integral transform to obtain families of distributions on other supports? Is there a need for new multivariate versions? This project, which can be taken in any of a subset of these or other directions, requires theoretical/methodological statistical knowledge, but should also be approached with a view towards practical application.

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