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