Potential PhD students are advised to contact me to discuss possible areas of research.
Over the past twenty years Bayesian statistics has seen a resurgence
in popularity largely due to the development of stochastic
methodologies capable of numerically approximating the necessary
integrals. A popular set of such methods are based on the construction
of a Markov chain with a stationary distribution proportional to the
posterior distribution of interest. Current interest is concerned
with the development of more efficient and more automatic
samplers. The ultimate aim is the determination of algorithms that,
given the required stationary distribution, will automatically
determine the most efficient methods of traversing both within and
between model spaces. Samplers that can additionally perform such
simulations on posterior distributions constructed from possibly
improper priors are another important goal.
Extreme value theory, as the name suggests, is concerned with the
analysis of the extreme levels of processes. Such processes where a
study of the very high level can be found in many areas. Some of these
might include the environment (extreme rainfall, wind speeds, tidal
surges, droughts, hurricaines, earthquakes etc.), finance (extremely
high or low log daily returns, risk analysis etc.) and physical manufacturing
processes (size of impurities in steel making). The analysis of such
processes is motivated by a set of models that hold asymptotically, in
analogue to the central limit theorem. While these models are useful
in quite general situations, there is considerable room for the
development of more flexible frameworks. There is particular scope for
development under a Bayesian framework, especially where prediction of
the process under study is of central interest. The above image
records the size of some of the rocks moved by flash floods, caused by
extreme levels of rainfall, in a storm over Vargas (in the central
coast of Venezuela) in December 1999.
Due to substantial leaps in technology over recent years, the
biological sciences are now routinely generating large amounts of
genetic-based data. The types of data being generated requires that
novel methodology be developed for their analysis. One such
illustration is the rapidly expanding field of microarray analysis,
whereby ''snap-shots'' of an individuals gene activity levels can be
captured through time or under different experimental settings (see
image). These data are typically high dimensional (many thousands of
genes), but low in the number of available replecations, and therefore
require the development of new techniques to analyse them.
Other application areas
include disease/trait gene mapping on genealogies, DNA-based analysis
of phylogenetic trees and issues involved in genetical database
searches.