Queen Mary, University of London School of Mathematical Sciences EPSRC CASE PhD Studentship in collaboration with Pfizer Global R&D Bayesian design and analysis of small multifactor industrial experiments Applications are invited for a PhD studentship funded by the Engineering and Physical Sciences Research Council and Pfizer Global R&D. Applicants must be EU residents and should have a good first degree in a subject containing a substantial amount of statistics and/or an MSc in Statistics. Some knowledge of the design of experiments or Bayesian statistics would be an advantage, but appropriate training will be given as necessary. The project is on the Bayesian design and analysis of factorial experiments. The student will work mainly at Queen Mary, University of London, under the supervision of Professor Steven Gilmour (http://www.maths.qmul.ac.uk/~sgg), but will also spend approximately three months at Pfizer in Sandwich, Kent (http://www.pfizer.co.uk), where the industrial supervisor will be Phil Woodward. The Statistics Group at Queen Mary is known internationally for its research in the design of experiments and Bayesian statistics and has extensive collaborations with industry, including long-standing links with Pfizer. The group has expanded over recent years and we now have a thriving group of PhD students in statistics (currently 5 full-time). We are in a large and diverse School of Mathematical Sciences, with over 50 academic staff, about 30 research staff and over 40 research students. We also have a number of joint projects with statisticians in the School of Medicine and Dentistry. A description of the project is given below. The studentship covers tuition fees for 3.5 years and, for UK residents only, living expenses of approximately £14,500 per annum (2004-05 rate). Application forms can be obtained online at http:///www.qmul.ac.uk/postgraduate/apply/index.html and informal enquiries can be made to Steven Gilmour (contact details below). Project Description ------------------- Multifactor designs, including fractional factorial and response surface designs, are the most widely used statistical contribution to industrial experimentation. They are used in many manufacturing and processing industries, including the pharmaceutical industry, where they are used both in pre-clinical research and in process improvement in manufacturing. They are increasingly recognised by scientists and engineers as allowing considerable information about the effects of several factors on the response to be obtained with a relatively small number of runs. The use of a particular type of design depends on how many factors are to be varied, how many levels each factor has, how much resource is available and how much has to be learned about the process under study. As in any other type of experiment, in the analysis of data from multifactor experiments, account must be taken of nuisance effects, such as block effects or time trend effects. At the design stage, a design should be chosen to be as nearly orthogonal as possible to the nuisance effects. The aim of this project is to improve the guidance available to experimenters in choosing a good design and in analysing data by using Bayesian methods, for both the design and analysis, especially when there is commercial pressure to minimise the size of the experiment. Fully Bayesian methods are rarely used in multifactor experiments, although a general setup for the analysis has been proposed. The proposed project will involve the investigation of three main areas: 1. Treatment designs. The statistical tools available for designing experiments usually choose a design which is optimal given the number of factors, the number of levels of each factor and the number of runs available. However, in practice, these are not given, but must be decided by the experimenters. This is usually done informally by looking at what can be obtained from various designs of different sizes and then making a decision on what seems sensible. A decision theoretic approach, involving Bayesian design, will be explored to allow a more informed choice of design to be made. A comparison of the decision theoretic methods with simple rules of thumb will be made to determine when the more complex approach is necessary. 2. Bayesian data analysis. In small experiments it often happens that there are few degrees of freedom available for estimating some of the nuisance effects. There is virtually always some prior knowledge about the sizes of nuisance effects and using this in a fully Bayesian data analysis seems natural. A comparison of the results obtained with those from standard analysies will be made to assess the benefits of the fully Bayesian analysis. 3. Designs allowing for nuisance effects. Given the Bayesian data analysis explored in 2, the design ideas in 1 can be modified to take account of the nuisance effects and the analysis that will be done. The methodology developed will be tested on historical data sets and will be put into practice as and when opportunities arise in experimental work at Pfizer. Steven Gilmour -- Professor Steven G Gilmour School of Mathematical Sciences Queen Mary, University of London Mile End Road London E1 4NS United Kingdom Tel: +44 (0)20 7882 7833 Fax: +44 (0)20 8981 9587 (department fax, not private) Web page: http://www.maths.qmul.ac.uk/~sgg