In many models, variances are assumed to have constant values although
this assumption is often unrealistic in practice. Joint modeling
of means and variances is difficult in many learning approaches, because
it can give rise to infinite probability densities. In Bayesian MCMC methods
where sampling is employed, the difficulties with infinite probability
densities are avoided, but these methods are not efficient enough for very
large models. Our variational Bayesian method, which is based on the building
blocks framework, is able to jointly model both variances and means
efficiently (Valpola et al., 2004).

The basic building block in our variance models is the variance node, which
is a time-dependent Gaussian variable controlling the variance of another
time-dependent Gaussian variable. The variance node can be used together
with our other Bayes building blocks to construct various hierarchical
models for the variances. Such models are introduced and discussed in (Valpola et al., 2004).
In this paper, we have applied them to biomedical MEG data consisting of
magnetic measurements of human brain signals contaminated by various artefacts.
The experiments in (Valpola et al., 2004) clearly demonstrate the existence of variance sources
in such a data.

The above figure shows two examples of models where variance nodes are
employed. On the left, the variance node generates a supergaussian density
to the source and hence enables the model to perform source separation.
On the right, the noise process of the observations is also conditioned
on the sources.

### References

H. Valpola, M. Harva, and J. Karhunen, "Hierarchical models of variance
sources". *Signal Processing* vol. 84, no. 2, 2004, pp. 267-282.
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