Mathematical Statistics
Members
Description
Research is focused in the areas of Bayesian Statistics, Design of Experiments and Process Control. Current areas of interest in Bayesian statistics include degradation modelling and diagnostics for model choice. In Design of Experiments, research interests include connectivity and robust design choice when observation loss is likely. In all research areas, particular emphasis is given to medical and industrial applications of theoretical results.
Bayesian statistics
Theoretical research in this area has focused on Bayesian diagnostics and classification. Particular emphasis and attention has been given to Bayes factors for normality diagnostics and Bayesian classification based on conditional predictive ordinates. Recent research has investigated the effect, on a Bayes factor, of omitting observations in time series models.
Design of experiments
A problem which is commonly encountered during experimentation is that of observation loss, the consequence being that the eventual experimental design is different from the design that was selected originally. If the eventual design is disconnected with respect to a class of treatments then linear unbiased estimates of some treatment comparisons will not exist and the experimental objectives are seriously compromised. Research in this area has centred on the identification of rank reducing observation sets for a large class of designs and on specification of staircase structures which summarize the connectivity properties for row-column designs. Pilot procedures have been developed for use at the planning stage to assess the vulnerability of a design to become disconnected. Cross-over designs, which are widely used in pharmaceutical experiments and clinical trials, and factorial designs, which are used extensively in industrial experimentation, are amongst the design types which have been investigated.
Medical statistics
Statistical analyses of medically orientated research projects, performed in collaboration with other departments within the university, have elicited publications in the fields of Biochemistry, Nutrition Technology, Pharmacology, Epidemiology and Public Health. Projects encompass retrospective studies, prospective studies and randomised controlled trials. The frequent presence of longitudinal data necessitates the use of repeated measures techniques in addition to the statistical tests typically associated with surveys and clinical trials.
Statistical computing
Computational algorithms for the identification and specification of the rank reducing observation sets in linear models are being developed for application to different types of experimental design. These algorithms form the core for programs which are intended to be made available generally on the website of the Mathematics Department. It is expected that the practitioner will have the dual option of focusing either on the whole design or on problem areas of the design.
Within the group there is extensive experience of a variety of statistical packages including R, SPLUS, MINITAB, SPSS and SAS.
Statistical process control
Statistical process improvement and control by exponentially weighted moving average (EWMA) methods is generally useful under various types of stable model behaviour, however results of limited use are obtained if the underlying output process is subject to occasional shifts in level leading to sustained random drift. In collaboration with statisticians from other UK universities, research at Surrey has involved investigation replacement of the EWMA predictor by a local level model and the development of feedback adjustment schemes. Proposed state space models have properties similar to the EWMA under stable conditions, but with the versatility to detect and respond to shifts in level leading to sustained random drift.
