Some idea of specific topics can be obtained by refering to the list of current and past Research Students, many of whom maintain their own pages which are linked. However, these specific topics are of course not available as new PhD topics though occasionally there are follow-on possibilities. Many of the topics of MSc dissertations have led (or may lead) to PhD topics so it is also useful to look there. I usually have one or two very specific proposals in mind which are not described below and which I can send direct to applicants on request if you contact me. The majority of former PhD students listed on the main page are pursuing research careers in academic or industrial environments, both within the UK and outside the UK (in roughly equal numbers).

The general areas for PhD topics in which I am interested are in Applied Statistics where the objective is the development of new statistical methodology to meet the demands of analyzing data effectively and efficiently. Areas of application where such data-driven problems arise include environmental statistics (e.g. geology, archaeology, climatology), medical statistics (e.g. clinical trials, survival data modelling), bioinformatics (e.g. analysis of microarray gene expression data, proteomics, metabonomics, biomedical imaging, High Throughput Screening, High Content Cell Biology). Statistical topics arising in these areas include multivariate methods, outliers and robust methods, linear functional models (i.e. 'errors-in-variables models'), spatial analysis, particle size analysis, time series, image analysis, non-parametric and semi-parametric density estimation. A few more details on some of these are given below.

Measurements of particles such as sand grains, blood platelets, fuel droplets and feedstuffs can provide information on depositional processes, diagnostics for coronary disease, combustion properties and explosive risks and digestibility of diets. Efficient statistical modelling of the size distribution can enhance the quality of the information extracted. Traditional models such as the log-Normal and Weibull for the size distribution are rarely good fits to the size distribution and so their use fails to extract available information. The log-hyperbolic family (which includes the log-Normal and log-skew-Laplace as special cases) has been found to be effective and to provide coherent answers to practical problems in a wide variety of fields. There remain many statistical problems in the area. For example, incorporating time-dependent covariates in the models, modelling more precisely the measuring techinque employed, especially those methods relying on light scattering where available mathematical approximations to light behaviour are only satisfactory at sizes well above those of interest in some applications.

Dendrochronology (or Tree-Ring Analysis) is based on the fact that many species of trees produce annual growth rings whose widths depend upon the climate of the growing season. Measurement of tree-rings can produce a sequence of records of past climate that can be used for plaeoenvironmental climatic reconstruction or for dating of old timbers. Statistical techniques used rely on various methods of time series analysis, especially methods of robust analysis that can overcome problems of data contamination.

Measurements of gene expression by recording the light intensities of perhaps many thousands of fluorescing genes implanted in a small chip or microarray introduce many statistical problems involving multivariate analysis of very high dimensional [megavariate] data with small numbers of observations and minimal replication. Statistical techniques of use in this area include multivariate analysis, Bayesian networks, Mixed Effects Linear Models. Measurement of protein or metabolic profiles by mass spectroscopic methods introduce problems of registration and calibration as well as those inherent in precursor technologies.

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Department of Probability and Statistics | School of Mathematics and Statistics | ||

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Dr Nick Fieller
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