The following seminars at UMIST are part of the Manchester
Centre for Statistical Science seminar programme. They are
held on Wednesdays at 2.15pm in room M12 of the Maths and
Social Sciences Building. All are welcome to attend.
23 October 2002
Statistical Models of Appearance for Image Analysis
Tim Cootes, ISBE, University of Manchester
Statistical models of shape and appearance have been shown
to be powerful tools for image interpretation, as they can
explicitly deal with the natural variation in objects of
interest. Such models can be built from suitably labelled
training sets. Given a model of appearance we can match
it to a new image using the efficient optimisation algorithms,
which seek to minimise the difference between a synthesized
model image and the target image. This talk will describe
the approach and recent developments, including examples from
the domains of face interpretation and medical image analysis.
6 November 2002
Prediction with mixture autoregressive models
Georgi Boshnakov, Maths, UMIST
Mixture autoregressive (MAR) models have the attractive property
that the shape of the conditional distribution of a forecast
depends on the recent history of the process. In particular,
it may have a varying number of modes over time. We find the
distributions of the multi-step predictors in MAR models. In
the important case when the MAR model is a mixture of normal
or, more generally, stable distributions, the multi-step
distributions are also mixtures of normal (respectively stable)
distributions. We will also discuss some issues arising from
multimodality.
13 November 2002
The effects of modelling pollution levels on the relative risks
obtained from time series studies examining the relationship
between air pollution and health
Gavin Shaddick (1, 3), Jon Wakefield (2,3)
(1) Department of Mathematical Sciences, University of Bath, UK
(2) Departments of Statistics and Biostatistics, University of
Washington, USA
(3) Department of Epidemiology and Public Health, Imperial
College of Science, Technology and Medicine, UK
In conducting time series studies to investigate the relationship
between air pollution and a health outcome, for example respiratory
mortality, it is important to have a good measure of the level of
pollution on any particular day. Often daily measurements are available
from a number of monitoring sites across the study. Each of these
monitors may measure different sets of pollutants, there may be periods
of missing data, and all of the recorded measurements will be subject to
error. Here, a (Bayesian) hierarchical model is used for the analysis of
such data, addressing the issues described, and specifically, allows
information from multiple sites on different pollutants to be combined.
This allows an estimate of a 'smoothed', or underlying pollution level
for each pollutant at each site to be obtained, incorporating any
possible lag structure, along with a measure of uncertainty. These
modelled levels of pollution can then be used in time series analyses
examining the relationship with health outcome. The measure of
uncertainty is particularly useful for accounting for the variation in
the pollution level, whether informally, when interpreting the
regression coefficients, or more formally via error-in-variables
modelling. These methods are applied to levels of a number of
pollutants, including PM10, CO, NO and SO2, measured at eight sites in
London for the period 1993-96. Associations between the resulting
modelled levels of pollution and daily mortality counts in London (from
1993-96) are then examined and compared with those obtained using the
original pollution measurements. The sensitivity of relative risks and
the width of their confidence intervals are examined with respect to
model assumptions, with particular interest in the effect of periods of
missing data.
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