UNIVERSITY OF GLASGOW

	    STATISTICS SEMINAR PROGRAMME

Wednesday, 19th April, 3 pm 

	Bayesian ecological regression analysis of environmental benzene 
	and childhood leukaemia: sensitivity to data inaccuracies, 
	geographical scale and ecological bias

	Nicky BEST (Small Area Health Statistics Unit, 
		    Imperial College School of Medicine)

Friday, 5th May, 3 pm (Glasgow-Strathclyde Partnership Seminar)
	
	Analyzing genomic regulatory behavior using cDNA microarrays

	Ed DOUGHERTY (Texas A&M University) 

Wednesday, 24th May, 3 pm
	
	Regularised local linear prediction

	Dimitris KUGIUMTZIS (University of Glasgow)

Wednesday, 7th June, 3 pm 

	Groebner basis method in statistics
	
	Henry WYNN (University of Warwick) 

Seminars take place in	Room 1f(203), Mathematics Building, 
			University of Glasgow

For further information please contact the seminar organiser:

Ilya Molchanov
University of Glasgow		: e-mail: [log in to unmask]	
Department of Statistics	: Ph.: + 44 141 330 5141
Glasgow G12 8QW			: Fax: + 44 141 330 4814
Scotland, U.K.			: http://www.stats.gla.ac.uk/~ilya/



   ABSTRACTS

BAYESIAN ECOLOGICAL REGRESSION ANALYSIS OF ENVIRONMENTAL BENZENE 
AND CHILDHOOD LEUKAEMIA: SENSITIVITY TO DATA INACCURACIES, 
GEOGRAPHICAL SCALE AND ECOLOGICAL BIAS

Benzene is classified as a Group 1 human carcinogen by the
International Agency for Research on Cancer, and it is now
accepted that occupational exposure is associated with increased
risk of various leukaemias. However, occupational exposure
accounts for less than 1% of all benzene exposures, the major
sources being cigarette smoking and vehicle exhaust emmissions. 
Whether such low level exposures to environmental benzene are
also associated with leukaemia risk is currently not known.
In this study, we investigate the relationship between benzene
emmissions arising from outdoor sources (predominantly road traffic 
and petrol stations) and incidence of childhood leukaemia in
Greater London. An ecological design is used due to the rarity
of the disease and the difficulty of obtaining individual-level
measurement of benzene exposure. However, a number of methodological
difficulties were encountered, including problems of case
registration errors, choice of geographical areas for analysis,
exposure measurement error and ecological bias. We use a Bayesian
hierarchical modelling framework to address these issues, and
investigate the sensitivity of our inference to the various modelling
assumptions.
(joint work with S. Cockings, J. Bennett, J. Wakefield and P. Elliott)


ANALYZING GENOMIC REGULATORY BEHAVIOR USING cDNA MICROARRAYS

Sequences and clones for over a million expressed sequence tagged
sites (ESTs) are currently publicly available. Functional
characterization of these genes lags behind the ability to collect
them. One way of gaining insight into a gene's role in cellular
activity is to study its expression pattern in a variety of
circumstances and contexts, as it responds to its environment and to
the action of other genes. cDNA microarrays facilitate large scale
surveys of gene expression in which transcript levels can be
determined for thousands of genes simultaneously. Since transcription
control is accomplished by a method which interprets a variety of
inputs, we require analytical tools for expression profile data that
can detect the types of multivariate influences on decision-making
produced by complex genetic networks. This talk will describe the
microarray technology and image analysis techniques used to quantify
expression levels. It will describe some analytic tools currently
being used, with emphasis on nonlinear multivariate prediction.



REGULARISED LOCAL LINEAR PREDICTION

Local linear prediction is one of several methods that have been
applied to prediction of real time series including financial time
series.  The difference to the global linear prediction is that, for
the estimation of the parameters of the linear autoregressive (AR)
model, only a number of scalar data segments from the history are
utilised.  These data segments correspond to points close to the
target point when the time series is viewed in a pseudo-state space
with dimension the order of the local AR model.

The parameters of the model are typically estimated using the ordinary
least squares (OLS). Apart from potential linearisation errors, a
drawback of this approach is the high variance of the predictions
under certain conditions. It has been shown that a different set of
so-called linear regularisation techniques, originally derived to
solve ill-posed regression problems, gives better predictions than OLS
on noisy chaotic time series. These methods reduce the variance
compared to OLS, but introduce more bias. A main tool of this analysis
is the Singular Value Decomposition (SVD), and a key to successful
regularisation is to damp the higher order SVD components.

In this seminar, I will describe the general features of local linear
prediction and particularly the OLS solution and some of its
regularisations. I will also show local linear predictions with OLS
and regularised solutions on some well-known real data sets.


GROEBNER BASIS METHOD IN STATISTICS

It is a good prediction that computational algebraic geometry will
find an increasing role in stastistics. In particular, Groebner bases
(G-bases) have proved useful in two areas: experimental design and
discrete statistical models such as contingenecy tables. The talk will
review the contents of a forthcoming monograph (Riccomomagno, Pistone
and Wynn) which pulls together the reseacrch of the authors over
around 5 years starting with the Pistone and Wynn (1996, Biometrika)
paper, covering experimental design, and more recent material on
probablity and statistics, complementary to the work of Diaconis and
Sturmfelds. The starting point is to represent a design, or the
support of a discrete distribution in the stochastic case, as a zero
dimensional polynomial ideal: the solution of a set of polynomial
equations. Ring quotient operations, which turn out to be critical,
can then be carried out using the G-basis methods on computational
algebra packages like Maple or the more specialised CoCoa.



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