- New approaches to inference in hidden Markov models. Hidden Markov models (HMMs) have become indispensable in signal processing and communications, speech recognition, natural language modelling, and computational biology and bioinformatics, and continue to find new applications, for example, in information security. Recent developments in HMM theory and practice include discovery of limiting Viterbi processes and various hybrid methods of inference about hidden path and model parameters. These have opened up opportunities for further theoretical and applied investigation. Depending on the candidate's background and aspirations, this project can focus more on the theoretical or applied component. A possible application is computational biology benefiting from a collaboration with the Computer Science Department of Royal Holloway. The project will also be benefiting from our continuing collaboration with the Institute of Mathematical Statistics of Tartu University (Estonia).
- On-line estimation in times series models. The aim of the project is to develop new parameter estimation methods for some important classes 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. The project aims to develop procedures that are recursive and, unlike some other methods, do not require storing all the data. These procedures would naturally allow for on-line implementation, which is particularly convenient for sequential data processing. In particular, this project would focus on development of new recursive procedures for parameter estimation in autoregressive time series models, and explore possibilities of extending these ideas to derive new estimation procedures in ARMA models.
- Statistical classification of human skin tissue using innovative imaging modalities. Raman spectroscopy is on its way to becoming the most effective imaging modality for computer aided diagnosis and surgery of skin cancer. Operating with small amounts of data, pilot studies focused on reliable detection of tumour, and had to employ simple classification approaches. As more data are now being acquired and annotated, more specialized classification of skin tissue becomes possible without jeopardizing the overall reliability. In this project, statistical and machine learning approaches would need to be applied in order to realize the anticipated gains in classification accuracy and reliability. The project is to be closely coordinated with a multidisciplinary team of researchers and medical practitioners from Nottingham University (Nottingham, UK). A successful candidate would need to contribute an increasingly strong expertise in statistical and machine learning, including hands-on data analysis skills. Familiarity with Matlab and confidence in programming in Matlab or a similar environment are highly desirable. The project will also benefit from the links with the Computer Science Department of Royal Holloway, which has an internationally recognized track record in machine learning.
- Statistical analysis and modeling of complex environments with application to Diffusion Weighted Magnetic Resonance Imaging (DWMRI). Diffusion Weighted Magnetic Resonance Imaging (DWMRI) extends the conventional MRI by measuring diffusion. Resulting diffusion profiles in turn allow us to estimate local structure of analysed matter, such as the human brain. Advanced statistical methods, such as inference on non-Euclidean manifolds, have been applied to make this estimation possible. Depending on the candidate's background and interests, this project can focus more on development and investigation of new statistical models and approaches inspired by DWMRI or on extensions of the existing models and methods and their novel applications to particular brain studies. In the latter case, links with the Brain and Behaviour Group of the Psychology Department of Royal Holloway and with St George's Medical School, University of London, should be particularly beneficial.
- Invariance and Symmetry in Statistical Modeling. Algebraic statistics emerged fairly recently and now covers a broad range of problems where methods of abstract algebra and computational algebraic geometry offer unique insights into probabilistic and statistical models and methods. One particular development takes advantage of the theory of polynomial invariants of finite groups in order to incorporate respective modes of invariance into probabilistic models and related statistical inference procedures. This project would investigate relevance and suitability of these ideas for various classes of statistical models and approaches, as well as particular applications, such as in statistical image analysis and computer vision.