TWO PhD STUDENTSHIPS IN STATISTICS
Applications are invited for two three-year full-time PhD studentships
at the Open University, Milton Keynes, starting on or before 1 October
2006. We offer the following four research projects; details of these
are given at the end of this message. If you have your own research
proposal, we will consider that as well.
1. Fitting New Families of Distributions to Data. Supervisor: Professor
Chris Jones.
2. Interpretable and Fast Dimensionality Reduction for Data of High
Dimension. Supervisor: Dr Nickolay Trendafilov.
3. A Computational Information-Geometric Approach to Sensitivity
Analysis in Statistical Science. Supervisor: Professor Frank Critchley.
4. Rotational Approach to Independent Component Analysis. Supervisor: Dr
Nickolay Trendafilov.
Applicants should have at least a 2(i) honours degree or a recognised
postgraduate qualification containing a substantial element of
statistics. The studentships will be based at the main Open University
campus in Milton Keynes. Although the Open University differs from other
universities in that we don't have undergraduate students on site, we
are in other ways similar to other universities. In particular, we have
a very strong and active Statistics Department. For more information
about the Department, see our website at http://statistics.open.ac.uk/ ,
or email Paddy Farrington at [log in to unmask]
Full tuition fees and research expenses will be paid, and a maintenance
grant will be payable, starting at 12,300GBP in 2006/7. There are no
nationality or residency restrictions.
To obtain an application form and the Open University's Research Degree
Prospectus, please email [log in to unmask], or phone +44
(0)1908 653844, or write to:
Val Spearman, Department of Statistics, Faculty of Mathematics and
Computing, Walton Hall, The Open University, Milton Keynes MK7 6AA.
You can also download the prospectus and application form from
http://www.open.ac.uk/research-degrees/ .
Where the application form asks for details of your research topic,
simply state which (one or several) of the four projects you are most
interested in, and why. Alternatively, include your own project
proposal. Completed application forms should be marked RDGI and returned
by 24 February 2006 to Val Spearman at the address above (or emailed to
[log in to unmask]).
Equal Opportunity is University Policy.
PROJECT SUMMARIES
1. "Fitting New Families of Distributions to Data"
The supervisor of this project is Professor Chris Jones who has recently
been developing new three- and four-parameter families of distributions
with a variety of skewness/tailweight properties for use in statistics.
As such, these provide a parametric modelling alternative to robust
statistics as usually practised. The project will emphasise practical
issues in the fitting of these distributions to data using maximum
likelihood. A large variety of questions arise: (i) in symmetric cases,
to what extent can the scale parameter be disentangled from tail
parameters? (ii) asymmetry is more easily handled, but does its
inclusion cause any extra difficulties? (iii) how best should the
distributions be parametrised? (iv) how useful are asymptotic formulae
in this context? (v) how best should these distributions be deployed in
regression contexts? (vi) might one base quantile regression on them?
(vii) is there any need for further new distributions or multivariate
versions? An important outcome will be the provision of user-friendly
software in a popular language such as, for example, R.
2. "Interpretable and Fast Dimensionality Reduction for Data of High
Dimension"
When analyzing large data one faces two types of related problems. The
number of the input variables is so large that the application of the
standard techniques becomes computationally too demanding. Even if the
computation time is not an issue the solutions produced are difficult to
interpret as involving too many of the input variables.
The aim is to develop two types of methods producing either approximate
sparse solutions of the standard multivariate techniques, or
transforming their exact solutions into interpretable ones, e.g. sparse
principal components or canonical variates with discrete loadings or
taking values 1, -1 and 0 only. They are appropriate for large data
because these solutions are close to the exact ones but much easier to
compute (the latter type of methods) and interpret (the former).
Particular interest will be paid to discrimination techniques because
the initial grouping of the large data seems to be a very reasonable
"pre-processing" strategy.
Application will be sought in areas as shape, image, handwritten
character recognition; multivariate analysis of microarray data; text
analysis; decision making units in management applications.
3. "A Computational Information-Geometric Approach to Sensitivity
Analysis in Statistical Science"
Perturbations of problem formulations in statistical science are always
pertinent. Accordingly, sensitivity analyses are sensible. This
cutting-edge interdisciplinary project is to use the latest developments
in information geometry to move towards fully invariant
local-through-global sensivity analysis, delivered to the practitioner
via a unified set of software tools. Generalised linear models have been
chosen as the primary focus of this work since they are perhaps the most
commonly used by applied statisticians and practitioners today. The
successful PhD applicant will work, with a computational emphasis, as
part of a team of leading international experts including Professor
Frank Critchley (Open University), Professor Paul Marriott (Waterloo,
Canada) and an Open University research fellow. The profile required is
a firm grounding in Statistics and good skills in developing programs in
statistical software such as R. Additional training, including any
necessary geometrical background, will be provided where needed.
4. "Rotational Approach to Independent Component Analysis"
Independent component analysis (ICA) is a latent variable model
developed in the signal processing community and is very similar to the
exploratory projection pursuit introduced by statisticians. The ICA
formulation is closely related to principal component analysis (PCA) and
factor analysis (FA). The key difference is that the ICA latent factors
are assumed independent.
Recently the ICA was reformulated as a specific rotation method: rather
than optimize a criterion applied to the loadings as in PCA and FA, a
criterion applied to the factors is optimized. This approach has to be
studied additionally and compared to a number of existing computational
methods for ICA. The main goal will be to apply this rotational approach
for studying the less developed "noisy" version of ICA.
ICA can be used in exploratory problems for clustering variables along
with the standard PCA. ICA can outperform PCA in recovering noisy
images. Together with Procrustes techniques it can be applied to a
number of recognition tasks, e.g. data from CCTV cameras, neuroimaging,
etc. Application to such data sets will be sought. The motivation of the
ICA application to social sciences problems seems problematic so far. It
will make sense to explore this potential area where PCA and FA are the
standard analytical tools.
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