The following research studentship, along with some others, was
advertised in the Guardian, on Tuesday (18/7/00).

The closing date for applications is: 28th July

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University of Hertfordshire
===========================

Business School
===============

Research Studentship in Statistics
==================================

``Statistical Modelling of Hybrid Spatial Processes''

Background
==========

Some commonly encountered types of spatial process are:  point
processes which generate points in space; lattice processes
which generate random surfaces in space; and fibre processes
which generate lines, or more generally, curves in space.
Examples of patterns that can be modelled using point processes
are locations where storms start and residential locations of
people who suffer from asthma. Examples of patterns that can be
modelled using lattice processes are altitude measurements and
concentrations of atmospheric pollutants obtained at regular
intervals in space. Examples of patterns that can be modelled
using fibre processes are river and road networks. Hybrid
processes arise when two or more of the above types of process
are considered simultaneously. For example, locations where
storms start can be related to measurements of altitude using a
point-lattice process, and it may be of interest to relate
residential locations of people who suffer from asthma to their
proximity to major roads using a point-fibre process.

Statistical methods for modelling point processes and lattice
processes individually are well established. In particular, a
technique called spectral analysis has been used successfully
with both types of process (Mugglestone and Renshaw, 1996a, b,
1998). Recent work has extended the spectral approach to deal
with point-lattice processes (Kanaan, 2000; Kanaan, Taylor,
Mugglestone and Goulard, 2000). Methods for modelling fibre
processes are less well developed, but conceptually they too can
be analysed by spectral methods. This project will develop
spectral methods for modelling fibre processes, and extend
recent work on point-lattice processes to deal with other types
of hybrid process.

Programme of Work
=================

Modelling fibre processes
-------------------------
The first step will be to extend the spectral approach to deal
with fibre processes. The best way of doing this may be to
represent each fibre by pattern points scattered along its
length (Stoyan, Kendall and Mecke, 1995). The spectral
properties of the fibre process can then be obtained via the
spectral properties of the representing point process. Another
option would be to obtain a lattice process based on the number
of fibres in each square of a grid. Properties of interest
include the mean length of fibres and any directional
preference.

Modelling point-fibre processes
-------------------------------
Once the spectral properties of fibre processes have been
established, the analysis of point-fibre processes can be
studied in much the same way as point-lattice processes. The
analysis of point-lattice processes has been developed by
Kanaan, Taylor, Mugglestone and Goulard (2000).

Applications
------------
The proposed supervisory team already has meteorological data to
work with (storm locations, durations and topography),
ecological data (tree species, size and altitude). Data for
applications in environmental epidemiology will be sought.
Basic fibre process work can also include industrial
applications, such as data on fibres in paper and other
materials. In these applications, the mean length of fibres
and a preferred direction for fibres may be related to the
strength of the product.  This, in turn, could be used, for
example, to determine which type(s) of tree a paper
manufacturer should buy or grow.

Supervisory Team
================

Internal Supervisor
-------------------
Dr. Paul C. Taylor (Senior Lecturer in Statistics, Department
of Statistics, Accounting and Management Systems, Business School,
University of Hertfordshire)

External Supervisor
-------------------
Dr. Moira A. Mugglestone (Senior Statistician/Epidemiologist,
MRC Institute for Environment and Health, Leicester)

References
==========

Mugglestone, M.A. and Renshaw, E. (1996a). A practical guide to
	the spectral analysis of spatial point processes.
	Computational Statistics and Data Analysis, 21, 43-65.

Mugglestone, M.A. and Renshaw, E. (1996b). The exploratory
	analysis of bivariate spatial point patterns using
	cross-spectra.	Environmetrics, 7, 361-377.

Mugglestone, M.A. and Renshaw, E. (1998). Detection of geological
	lineations on aerial photographs using two-dimensional
	spectral analysis.  Computers and Geosciences, 24,
	771-784.

Kanaan, M.N. (2000). Cross-spectral analysis for point-lattice
	processes.  Ph.D. Thesis, The Open University.

Kanaan, M.N., Taylor, P.C., Mugglestone, M.A. and Goulard, M.
	(2000).  Cross-spectral analysis of point-lattice
	processes (in preparation).

Stoyan, D., Kendall, W.S. and Mecke, J. (1995). Stochastic
	Geometry and its Applications, Second Edition.
	New York: Wiley.

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The research studentship is tenable for three years.  An annual bursary
is payable, funded by the Business School at the University of 
Hertfordshire, which will be 7,850 pounds in the 2000/2001 session;
University registration fees are waived.  The successful candidate must
possess a good first degree, or a masters degree, and will be required
to register for a research programme, leading to the award of a PhD
(subject to University Regulations).  The starting date is on or before
1st October 2000.

For further details and an application form for the studentship, please
contact Mrs Ruth Grillo, Business School, University of Hertfordshire,
Mangrove Road, Hertford, Herts. SG13 8QF, quoting the reference A.





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