PhD Research Topics in Statistics

The following are a selection of research topics that have been put forward by supervisors and are available for suitably qualified students to take up. If one of these projects interests you, then please contact the supervisor listed to discuss what it entails and whether it is still available. We will also consider topics suggested by students and can devise other projects connected with the research interests of the Department. In addition, note also that this list is not exhaustive since many supervisors have not listed their projects here.

Robust Estimation in ARCH Models

Supervisor: Dr Kanchan Mukherjee

A common characteristic of time series data is that the instantaneous variability, called the volatility of the series, is not constant over time but depends strongly on its immediate past. In his seminal work, Nobel Laureate (for the year 2003) R. F. Engle (1982, Econometrica) modeled volatility of a time series by a linear combination of the squares of its immediately past observations and named it the Autoregressive Conditional Heteroscedastic (ARCH) Model. A PhD project in this area could involve investigation of the robust estimation procedures of the underlying regression and variance parameters in a nonlinear regression model with errors exhibiting ARCH effect. Numerical as well as theoretical properties can be studied in details based on weak convergence properties of certain randomly weighted empirical processes.

Multiple Classifier Systems

Supervisor: Dr Idris Eckley

This project will research the theory and application of multiple classifier systems. The project is jointly funded by a FTSE 100 consumer goods company and the EPSRC. Thus, in addition to the usual PhD experience, this will provide an opportunity for you to occasionally work at the company’s site to understand how these tools might be applied in an industrial R&D setting.

Identification of Causal Genetic Variations on Heart Disease

Supervisor: Dr Thomas Jaki

Personalised medicine aims to tailor treatments based on the individual patient’s specific characteristics and is one of the key development areas in health care. New technological developments in the past decade enabled fast and inexpensive genotyping allowing genetic factors to be considered for personalisation of treatments. Single nucleotide polymorphisms (SNPs) are variations in the DNA sequence that occur when a single nucleotide in the genome sequence is altered. The impact of SNPs can be large as they are often related to diseases and to differences in how individuals respond to a therapy or drug. It therefore is of major interest to identify SNPs responsible for these differences in the outcome in order to determine the optimal treatment and dosage.

Based around a collaborative clinical research project in heart disease, this project aims to develop statistical methods for identification of causal SNPs in genotype-phenotype association studies. These relationships are essential for the effective development of specialised treatments and personalisation of doses and treatment regimes.

Developing Valid and Reliable Assessment Tools for Use in Children

Supervisor: Dr Gillian Lancaster

There are many issues related to the measurement of outcomes for health evaluation particularly with respect to child health in developing countries. It has been estimated that more than 200 million children under five years fail to reach their potential in cognitive development because of poverty, poor health and nutrition and deficient care. Increasing evidence has shown that early interventions may help prevent the loss of potential in affected children. However, one of the drawbacks in the implementation of these interventions is the availability of tools to assess child development in non-Western settings. Western developmental assessment tools may be inaccurate when testing children in a different cultural setting, both in terms of the items tested and the normal reference values given for the population. We have developed the Malawi Developmental Assessment Tool (MDAT) and qualitative methods have highlighted that more culturally relevant items can be identified. Performance of these items has been examined using a simple graphical technique based on logistic regression with regression splines. The aim of this project is to develop methods for assessing the validity and reliability of the tool, and particularly to implement and contrast methods for scoring the stages of development of children in Malawi. The tool will be of benefit to community health workers in rural African settings as well as those looking at the developmental outcomes of children in sub-Saharan Africa.

References

• Gladstone M., Lancaster G.A., Jones A.P., Maleta K., Mtitimila E., Ashorn P. and Smyth R.L. (2008). Can Western developmental screening tools be modified for use in a rural Malawian setting? Archives of Disease in Childhood 93: 23 – 29.
• Lancaster G.A. Statistical issues in the assessment of health outcomes in children: a methodological review. Journal of the Royal Statistical Society A 172(4): 707-727.

Evidential Value of DNA Database Comparisons and the Effect of Background Sample Size on Comparison Problems.

Supervisor: Dr David Lucy

Recently there has been controversy over the evidential value of a DNA identification made from a database of DNA profiles. Two positions exist amongst the forensic community, a school of thought which suggests that the evidential value is lower, and one which says that discovery on a DNA database make little difference to the evidential value. The first half of this project would concern itself with approaches to finding a definitive answer to the seeming conundrum forensic scientists seem to have found themselves in.

The second half would be to look, through a variety of analytic and simulation approaches, at the effect of varying the size of database upon likelihood ratio estimates for general comparison problems.

Optimising Local Metropolis-Hastings Algorithms.

Supervisor: Dr Chris Sherlock

For non-routine problems in statistical inference the class of Metropolis-Hastings algorithms often provides the method of choice. The efficiency of a given Metropolis-Hastings algorithm can vary radically, not only from problem to problem, but also across the parameter space for a given problem.

Recent theoretical limit results for the random walk Metropolis algorithm have provided a general set of criteria such that the scaling for the proposed jump is optimised when the acceptance rate is 0.234. So far this work has considered a single scale parameter for the whole of the sample space and it requires that certain functional of the first and second derivatives of the log-target converge to fixed values: the optimal scaling is then a function of these values.

The research project concerns extending these results to more general targets and to more general local Metropolis-Hastings algorithms, allowing for (1) The scale parameter to vary as a function of the derivatives at the current point in the target and (2) An offset to be introduced into the proposal, which is also a function of the derivatives.

The primary objective of the project is to produce an optimally efficient generic scale/offset algorithm; this will be compared with two competing “scale and offset” algorithms: the MALA and Gamerman algorithms. A general result for the limiting optimal acceptance rate will also be sought.

Bayesian Methods for the Monitoring of Neuromuscular Disorders

Supervisor: Dr Gareth Ridall

A difficulty in the assessment of treatments of neuromuscular diseases such as Amyotrophic Lateral Sclerosis (ALS) (widely known in the UK as motor neurone disease) has been the lack of a reliable measure of disease progression. One such measure would be an estimate of the number of surviving motor units (Motor Unit Number Estimation, MUNE). Existing MUNE methods can assess longitudinal progression, but complexity, lack of applicability to all stages of disease and difficulty in accounting for motor unit instability in ALS have limited their widespread use. Furthermore, current methods are based on unrealistic and unsustainable assumptions. Ridall et al. (2006) and Ridall et al. (2007) describe a Bayesian statistical methodology by allowing the number of units to be an unknown of the model and using reversible jump Markov chain Monte Carlo to estimate the number of functioning motor units A by-product of this method is that it also describes the characteristics of populations of functioning motor units.

The objective of this research project is to develop a reliable automated statistical method of quantifying the number of motor units in a muscle that will allow monitoring of the progression of neuromuscular diseases in which motor units are lost. The method is non-invasive and applicable to routine clinical use. New statistical methodology will be required that incorporates information from multiple electrodes. The research outcomes from these investigations should have wider statistical application and they will lead to a better understanding of the physiology of motor unit activation.

References

• Ridall P G, Pettitt AN, Friel N, Henderson R D and McCombe P A. (2007) Motor unit number estimation using reversible jump Markov chain Monte Carlo (with discussion) Appl Stats, 56,1-26 [PDF]
• Ridall P G, Pettitt A N, Henderson R D and McCombe P A (2006). Motor unit number estimation-a Bayesian approach. Biometrics 62:1235-50.