We invite applications for two full-time three-year PhD studentships in Mathematics and Statistics commencing 1st October 2014. 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 £13,726 per annum + £1250 per annum to cover training and conference participation).



Overseas applicants are also welcome 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.



There are currently three PhD projects available in Statistics:



(1) Real time forecasting and monitoring of high frequency data

(http://www.mathematics.open.ac.uk/80256EE9006B7FB0/(httpAssets)/C161D4B5436F288380257C45003D38C4/$file/2014projectAF.pdf)

– Álvaro Faria;



(2) Application and comparison of transformations for orthogonality

(http://www.mathematics.open.ac.uk/80256EE9006B7FB0/(httpAssets)/465E9707D388EB0E80257C580041FC48/$file/2014projectPG.pdf)

– Paul Garthwaite; and



(3) Forecasting and monitoring traffic network flows

(http://www.mathematics.open.ac.uk/80256EE9006B7FB0/(httpAssets)/15C3470756931F2B80257C45003D6EC5/$file/2014projectCQ.pdf)

– Catriona Queen.



(Please see below for full details of each project.)



A research proposal is not required, but applicants should make clear which of the above projects is 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/index.htm and, in particular, 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, 28 February 2014.



Application forms are available from

http://www3.open.ac.uk/study/research-degrees/explained/how_to_apply/mphil_and_phd_application_process.htm





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Statistics PhD projects descriptions:



(1) Real time forecasting and monitoring 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 real-time high-frequency processes in various areas. Those include short-term electricity load forecasting in energy generation as well as wireless telemetric biosensing 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 real-time. There are a number of proposed NLAR forecasting models in the literature mostly non-dynamic and/or not appropriate for real-time 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 process nonlinearities. 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 the 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 covariates on the DSTAR models without compromising real-time applicability?

    - 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 nonlinearities 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 programing skills: current software for these models is written in R.



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(2) Application and comparison of transformations for orthogonality –

Supervisor: Paul Garthwaite



In statistics, having variables that are independent or uncorrelated can aid data analysis and the interpretation of results. Principal component analysis is the most common method of transforming a set of correlated x-variables to a set of quantities (the principal components) that are uncorrelated. A disadvantage of this transformation is that there is no close association between a principal component and an individual x-variable – each component typically relates to a number of x-variables and an x-variable may relate to more than one component.

Two recently proposed transformations are the cos-max transformation and the cos-square transformation. They each give orthogonal components and retain the identity of variables: each component is closely associated with a single x-variable and each x-variable is associated with a single component. One purpose of this PhD project is to discover and explore applications of these two transformations, initially focusing on regression. The transformations have different properties but typically give similar components. Another purpose of the project is to find conditions under which the properties held by one transformation are approximately held by the other.



This is a new area of research. To date the transformations have led to the following new methods (proposed in the references below): (i) a unified approach to the identification and diagnosis of collinearities, (ii) a method of setting prior weights for Bayesian model averaging, (iii) a means of calculating an upper bound for a multivariate Chebyshev inequality, and

(iv) a means of evaluating the contributions of individual variables in a quadratic form. The diversity of these applications illustrates the scope of the transformations.



The project will involve theoretical development of statistical methodology and skills in certain aspects of matrix algebra will be developed. There will also be a large amount of practical work requiring the use of R.



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(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. This project aims to tackle some of the outstanding issues, such as the following.



    - Any change in traffic flows is often associated with an incident, such as a road traffic accident. Can a monitor be developed which can detect any unexpected changes in traffic flow? And can a monitor detect when a road is reaching capacity, so that congestion is likely to occur?

    - When traffic is flowing freely, upstream flows affect flows downstream. In times of congestion or when there is a road block, queuing vehicles can cause the relationships between flows at different locations to change so that downstream flows can affect upstream flows. How can a dynamic graphical model accommodate these changing relationships over time?

And how can these changes be detected?



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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