The non-Gaussianity of the cosmic shear likelihood - or: How odd is the
  Chandra Deep Field South?
  (abridged) We study the validity of the approximation of a Gaussian cosmic
shear likelihood. We estimate the true likelihood for a fiducial cosmological
model from a large set of ray-tracing simulations and investigate the impact of
non-Gaussianity on cosmological parameter estimation. We investigate how odd
the recently reported very low value of $\sigma_8$ really is as derived from
the \textit{Chandra} Deep Field South (CDFS) using cosmic shear by taking the
non-Gaussianity of the likelihood into account as well as the possibility of
biases coming from the way the CDFS was selected.
  We find that the cosmic shear likelihood is significantly non-Gaussian. This
leads to both a shift of the maximum of the posterior distribution and a
significantly smaller credible region compared to the Gaussian case. We
re-analyse the CDFS cosmic shear data using the non-Gaussian likelihood.
Assuming that the CDFS is a random pointing, we find
$\sigma_8=0.68_{-0.16}^{+0.09}$ for fixed $\Omega_{\rm m}=0.25$. In a
WMAP5-like cosmology, a value equal to or lower than this would be expected in
$\approx 5%$ of the times. Taking biases into account arising from the way the
CDFS was selected, which we model as being dependent on the number of haloes in
the CDFS, we obtain $\sigma_8 = 0.71^{+0.10}_{-0.15}$. Combining the CDFS data
with the parameter constraints from WMAP5 yields $\Omega_{\rm m} =
0.26^{+0.03}_{-0.02}$ and $\sigma_8 = 0.79^{+0.04}_{-0.03}$ for a flat
universe.
