The Centre of Biostatistics at the University of Limerick in conjunction
with the Department of Mathematics and Statistics invite you to the
final seminar in our spring series. Further details of the series are
available at www.ul.ie/biostatistics
Friday, May 2nd
2:00pm
A-2002
Fully Bayesian Source Separation with Application to the Cosmic
Microwave Background
Simon Wilson
School of Computer Science and Statistics
Trinity College Dublin
Blind source separation refers to the inferring of the values of sources
from observations that are linear combinations of them; it is an example
of Factor Analysis. Both the sources and the matrix of linear 'mixing'
coefficients may be unknown. Here we describe an approach where the
sources are assumed to be Gaussian mixtures, which may be independent or
dependent
- this leads to a model that is also known as a mixture of factor
analyzers. An MCMC procedure has been developed that implements a fully
Bayesian procedure e.g. it computes the posterior distribution of
sources, their Gaussian mixture parameters and the matrix of linear
coefficients from the data.
The method is applied to recovery of the cosmic microwave background
(CMB). The CMB is one of many sources of extraterrestrial microwave
radiation and we observe a weighted sum of them from the Earth at
different frequencies. Its accurate reconstruction is of great interest
to astronomers and physicists since knowledge of its properties, and in
particular its anisotropies, will place strong restrictions on current
cosmological theories. From the perspective of a Bayesian solution,
this application is interesting as there is considerable prior
information about the linear coefficients and the sources. Results from
the analysis of data from the WMAP satellite will be presented, where
microwave radiation is observed at
5 frequencies and separated into sources, including the CMB. A
discussion of the many outstanding issues in this problem is also
presented.
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