We invite applications for several full-time three-year PhD studentships in Mathematics and Statistics commencing 1 October 2015.
PhD students are based at the University’s Walton Hall campus in Milton Keynes, UK.
Studentships cover full-time fees and include a stipend (currently £13,863 per annum + £1250 per annum to cover training and conference participation).
Overseas applicants are also welcomed but those from a non-European Economic Area country that is not majority English-speaking must hold a
Common European Framework of Reference for Languages (CEFR) certificate for English at B2 level or higher at the time of applying.
Full details of projects are available from: http://www.mathematics.open.ac.uk/phd
There are currently three PhD projects available in Statistics:
(1) Bayesian dynamic forecasting of high frequency data – Álvaro Faria;
(2) F-G Distributions for Survival and Reliability Modelling – Prof. Chris Jones; and
(3) Forecasting and monitoring traffic network flows – Catriona Queen.
(Please see below for more detail of each project.)
A research proposal is not required, but applicants should make clear the project(s) of interest.
Interested persons with a strong background in Statistics are encouraged to make informal enquiries to [log in to unmask]
General information about studying for a research degree with the Open University is available from the Research Degrees Prospectus:
http://www3.open.ac.uk/study/research-degrees/explained/degrees_we_offer/doctor_of_philosophy.htm
Completed application forms, together with a covering letter indicating your suitability and reasons for applying, should be sent to:
[log in to unmask] to arrive by 5pm on Friday, 17 April 2015.
Application forms are available from http://www.open.ac.uk/postgraduate/research-degrees/how-to-apply/mphil-and-phd-application-process
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Statistics PhD projects descriptions:
(1) Bayesian dynamic forecasting of high frequency data – Supervisor: Álvaro Faria
With recent technological advances, there has been an increasing demand for statistical forecasting
models that can detect and quantify patterns, assess uncertainties, produce forecasts and monitor
changes in data from high-frequency processes in various areas. Those include short-term electricity load
forecasting in energy generation as well as wireless telemetric bio-sensing in healthcare where monitoring
of patients in their natural environment is desirable. Usually, many such processes are well modelled by
non-linear auto-regressive (NLAR) models that are dynamic and can be sequentially applied in near
real-time. There are a number of proposed NLAR forecasting models in the literature mostly non-dynamic
and/or not appropriate for high-frequency time series data applications.
Forecasting and monitoring data from high-frequency processes can be a multivariate non-linear time
series problem. This project takes a Bayesian approach to the problem, building up on recently proposed
analytical state-space dynamic smooth transition autoregressive (DSTAR) models that approximate the
underlying process non-linearities. DSTAR models have been shown to be promising for forecasting
certain non-linear processes (as described in the reference listed below), but issues still remain before
such models can be usefully adopted for assimilation of high-frequency data in practice. This project aims
to tackle some of the outstanding issues, such as the following.
- How to include information from co-variates on the DSTAR models without compromising demands for
fast computations?
- How to retain model interpretability in relation to STAR model parameters?
- How to effectively model multiple cyclic behaviour of different orders?
- How alternative approximations to non-linearities improve on the existing polynomial ones? Would
sequential simulation methods such as particle filtering provide appropriate answers?
Hourly electricity load data for a region in Brazil are available for the project. The project will involve
theoretical developments in statistical methodology, as well as a large amount of practical work requiring
good statistical programming skills: current software for these models is written in R and Mathematica.
(2) F-G Distributions for Survival and Reliability Modelling - Supervisor: Prof. Chris Jones
One of the most popular methods of creating families of univariate continuous distributions on the whole
real line R with parameters controlling skewness and tail weight has some of its antecedents in survival
and reliability modelling (where univariate data live on the positive half-line R^+). This method is a
generalisation of the probability integral transformation, which states that if U is uniformly distributed on
(0, 1), then X = G^-1(U) has distribution function G(x). The generalisation is to let U take a non-uniform
distribution F on (0, 1), depending on those extra parameters, so that X has distribution function F(G(x)).
The main supervisor currently prefers alternative methods of creating families of distributions on R but is
less sure of the relative worth of the described approach on R^+. The aim of this project would be to
explore the latter via a literature review, by exploring general properties of the families of distributions on
R^+ (in particular the shapes of their hazard functions), and through bespoke construction/choice of F to
work well on R^+. This project is principally theoretical/methodological, but with scope to pursue and
develop practical applications if successful in the former terms.
(3) Forecasting and monitoring traffic network flows - Supervisor: Catriona Queen
Congestion on roads is a worldwide problem causing environmental, health and economic problems.
On-line traffic data can be used as part of a traffic management system to monitor traffic flows at different
locations across a network over time and reduce congestion by taking actions, such as imposing variable
speed limits or diverting traffic onto alternative routes. Reliable short-term forecasting and monitoring
models of traffic flows are crucial for the success of any traffic management system: this project will
develop such models.
Forecasting and monitoring the traffic flows at different locations across a network over time, is a
multivariate time series problem. This project takes a Bayesian approach to the problem, using dynamic
graphical models. These models break the multivariate problem into separate, simpler, subproblems, so
that model computation is simplified, even for very complex road networks. Dynamic graphical models
have been shown to be promising for short-term forecasting of traffic flows (as described in the references
listed below), but issues still remain before the models can be used for an on-line traffic management
system in practice.
Minute-by-minute traffic flow data at a number of different locations at the intersection of three busy
motorways near Manchester, UK, are available for the project (kindly supplied by the Highways Agency in
England: http://www.highways.gov.uk/). The project will involve theoretical developments in statistical
methodology, as well as a large amount of practical work requiring good statistical programming skills:
current software for these models is written in R.
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