  As well as primary fluctuations, CMB temperature maps contain a wealth of
additional information in the form of secondary anisotropies. Secondary effects
that can be identified with individual objects, such as the thermal and kinetic
Sunyaev-Zel'dovich (SZ) effects due to galaxy clusters, are difficult to
unambiguously disentangle from foreground contamination and the primary CMB
however. We develop a Bayesian formalism for rigorously characterising
anisotropies that are localised on the sky, taking the TSZ and KSZ effects as
an example. Using a Gibbs sampling scheme, we are able to efficiently sample
from the joint posterior distribution for a multi-component model of the sky
with many thousands of correlated physical parameters. The posterior can then
be exactly marginalised to estimate properties of the secondary anisotropies,
fully taking into account degeneracies with the other signals in the CMB map.
We show that this method is computationally tractable using a simple
implementation based on the existing Commander component separation code, and
also discuss how other types of secondary anisotropy can be accommodated within
our framework.
