Department of Mathematics
Royal Holloway University Of London

Statistics and Probability Theory

The previously advertised funded PhD position in Applied Statistics and Probability Theory has been filled. Self-funded applicants may still be considered at any time. Please consult this list of possible research projects and general information on PhD research with Department of Mathematics at RHUL, including information on the application procedure. When submitting your application on-line, please make sure you choose 'PhD in Mathematics' and then specify 'Applied Statistics and Probability Theory' in the 'Research proposal' field. Informal inquires can be sent to Dr Alexey Koloydenko at Alexey.Koloydenko@rhul.ac.ukApplicants should have, or expect to receive, a first or upper second class degree in mathematics, statistics, computer science, or a closely related subject. Note that UK and EU nationals are entitled for reduced fees; for determining your status please consult this document.  While a successful applicant from outside EU would be liable for higher tuition fees, the Department will continue to seek additional funding to help such a candidate cover this difference.  Applicants are reminded that their Personal/Research Statement should attempt to connect their academic or professional background, interests, aspirations, and future plans to the subjects of the proposed projects. These projects might be considerably modified to accommodate interests of applicants with prior research experience.  

Current interests of the core members of our group are statistical image analysis, computational and algebraic aspects of statistical modeling and inference, including stochastic approximation and recursive parameter estimation for stochastic processes.

A specific example of our research is in the field of Diffusion Weighted Magnetic Resonance Imaging (DWMRI), which extends the conventional MRI by measuring diffusion. Resulting diffusion profiles in  turn allow us to estimate local structure of analyzed matter, such as the human brain. With the help of statistical methods and models, DWMRI has provided new  insights into developmental and pathological conditions of the human brain.  A principled way to organize information about diffusion at a location of interest is via Diffusion Tensor. As Diffusion Tensors form a non-Euclidean space, even the usual averaging becomes questionable when applied to multiple Diffusion Tensors. In collaboration with Nottingham University (UK) and the University of South Carolina (USA), we have been studying various methods, primarily based on the statistical shape theory, of doing meaningful statistics in the space of Diffusion Tensors. As a central result of this work, the paper "Non-Euclidean statistics for covariance matrices, with application to diffusion tensor imaging" appeared in  the Annals of Applied Statistics, an internationally leading journal. A member of our group gave invited seminars on this topic at Edinburgh University (UK), Tartu University (Estonia), and the local Computer Science Department. We have already supervised an MSc and MSci dissertations and a Nuffield Summer research student, and see several directions for potential PhD work in this area. Links with the Brain and Behaviour Group of the Psychology Department of Royal Holloway is also a positive factor for our future work in this area. 

Another interesting recent development which requires extensive statistical analysis is application of Raman spectroscopy to detection, diagnosis, and treatment of skin cancer. In collaboration with Nottingham University (UK), a pilot study has now been successfully completed as documented in the paper "Development of Raman micro-spectroscopy for automated detection and imaging of Basal cell carcinoma''  (Journal of Biomedical Optics, 2009, 14, 054031). This work provides abundance of material for a PhD dissertation to investigate advanced statistical and machine learning approaches to classification of skin cancer based on Raman Spectroscopy.  The project has recently been awarded a research grant from the Department of Health.

We have also been contributing to the theory and applications of hidden Markov models (HMMs). This work grew out of a past collaboration between Eurandom and Philips Speech Processing team. Hidden Markov models have become indispensable in, for example, signal processing and communications, speech recognition, natural language modelling, and computational biology and bioinformatics. Jointly with the Institute of Mathematical Statistics of Tartu University (Estonia), we have developed an asymptotic theory for the Viterbi decoding, the main mechanism of inference in HMMs. Based on this theory, we have also proposed new estimators for model parameters as well as new decoding protocols. The paper "A constructive proof of the existence of Viterbi processes''  has just appeared in IEEE Transactions on Information Theory and is indicative of our recent work in this area. Recent research visits to the University of Tartu have been funded by the Estonian Science Foundation. The most recent report can be found here.

Since our work on HMMs also concerns computational biology, we presented recent results in the Bioinformatics session of the 2009 Annual Conference of the Royal Statistical Society (RSS), who have also supported our contribution by a conference grant. This work also involves Computer Science Department of Royal Holloway, in particular gene-finding algorithms. A potential PhD project would concern new methods of inference in HMMs, and would involve both mathematical theory and computational experiments. 

Besides Diffusion Weighted MRI, we also maintain some involvement in Statistical Image Analysis and Computer Vision via the area of Natural Image Statistics. Thus, in January 2009 a member of our group gave an invited talk "Discrete Symmetries in Statistical Image Analysis and Beyond" at the ``Group Theory, Invariance and Symmetry in Vision'' technical meeting of the British Machine Vision Association and Society for Pattern Recognition. We would also be willing to supervise highly motivated PhD candidates with strong computer science backgrounds on topics related to natural image statistics.  More generally, we are also interested in roles invariance and symmetry play in probability theory and statistics and in particular how recent relevant developments in computational algebraic geometry lend themselves to probability theory and statistics.   

Our current research also includes new parameter estimation methods for an important class of statistical models, using ideas of stochastic approximation theory. Stochastic approximation is a method to detect a root of an unknown function when the latter can only be observed with random errors. We develop procedures that are recursive and, unlike other methods, do not require storing all the data. These procedures naturally allow for on-line implementation, which is particularly convenient for sequential data processing. One of the current projects aims to develop new recursive procedures for parameter estimation in autoregressive time series models using the methods of stochastic approximation, and also to explore possibilities of extending these ideas to  develop new estimation procedures in ARMA models.

Members of our group have also engaged in technical reviewing for IEEE Transactions on Image Processing, European Journal of Operational Research, Journal of Biological Engineering, Knowledge Transfer Networks/Industrial CASE Awards in Industrial Mathematics.

Further information can be found on the personal web pages of the individual members (see below). Please note also that other research groups of this Department, such as Quantum Dynamics, naturally interface with Statistics and Probability Theory.

Academic staff

Dr Teo Sharia

Prof. Peter Wild

Dr Alexey Koloydenko

Prof Sean Murphy

 

 

New PhD students

Lei Zhong

Ufuk Mat

 

 


Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX
Tel/Fax: +44 (0)1784 443093/430766