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The measurements vectors are assumed to be generated by a
linear mapping *A* from mutually independent source signals and additive Gaussian noise .
*x*(*t*) = *As*(*t*) + *v*(*t*)

The components *v*_{i}(*t*) of the noise are assumed to have means *b*_{i}
and variances . Another way to put this is to say
that *x*(*t*) has Gaussian distribution with mean *As*(*t*)+*b* and diagonal
covariance with components . Each component *A*_{ij}
of the linear mapping is assumed to have zero mean and unit variance.
The distribution of each source signal is a mixture of Gaussians (MOG).

The parameters *c*_{ij} are the logarithms of mixture coefficients,
*S* the means and the logarithms of the standard deviations
of the Gaussians^{} (here denotes a Gaussian distribution over *a* with mean *b* and
variance *c*).
The distributions of parameters *c*_{ij}, *S*_{ij}, ,*b*_{i} and are ,, , and .

The prior distribution of the hyperparameters , ,, , *B*, , and is assumed to
be uniform in the area of reasonable values for the hyperparameters.

To summarise: the eight hyperparameters are assigned flat prior pdfs.
The distributions of other parameters are defined hierarchically from
these using Gaussian distributions each parametrised by the mean and
the logarithm of the standard deviation. The joint pdf of is simply the product of the independent pdfs.

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*Harri Lappalainen*

*7/10/1998*