Seminário
PIPGEs ? UFSCar-USP ? 16/12/2013 - 14h30
LOCAL:
ICMC-USP
? Bloco 4 ? Auditório Prof. Luiz Antonio Fávaro
TÍTULO:
A Bayesian approach
to indirect imaging problems with applications in
engineering
PALESTRANTE:
Robert G. Aykroyd,
Department of Statistics, University of Leeds, UK and
Editor of the Journal
of Applied Statistics
RESUMO:
The
use of non-invasive techniques for the monitoring of an industrial process is
widespread. Such techniques produce a safe, cheap and fast method for the
visualization of the internal features from external measurements. These inverse
problems, however, are often a substantial mathematical challenge and can be
ill-posed, with more unknowns than data values, and ill-conditioned, with high
correlation between variables. This results in problems where either there is no
unique solution or where the solution does not depend continuously on the data.
One approach is to re-parameterize the model to produce a well-posed problem and
to include additional information through prior modelling. Estimation is based
on the resulting posterior distribution which can be explored using a Markov
Chain Monte Carlo algorithm. This talk will describe the Bayesian approach to
image reconstruction in inverse problems with a range of examples used for
motivation from archaeology and medicine, as well as engineering. Two examples
will be considered in detail: the mixing of fluids in a tank, and the separation
of water and oil in a hydrocyclone. These will highlight the wide range of
possible modelling approaches and possible summary
output.
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