Cosmological parameters, shear maps and power spectra from CFHTLenS
  using Bayesian hierarchical inference
  We apply two Bayesian hierarchical inference schemes to infer shear power
spectra, shear maps and cosmological parameters from the CFHTLenS weak lensing
survey - the first application of this method to data. In the first approach,
we sample the joint posterior distribution of the shear maps and power spectra
by Gibbs sampling, with minimal model assumptions. In the second approach, we
sample the joint posterior of the shear maps and cosmological parameters,
providing a new, accurate and principled approach to cosmological parameter
inference from cosmic shear data. As a first demonstration on data we perform a
2-bin tomographic analysis to constrain cosmological parameters and investigate
the possibility of photometric redshift bias in the CFHTLenS data. Under the
baseline $\Lambda$CDM model we constrain $S_8 =
\sigma_8(\Omega_\mathrm{m}/0.3)^{0.5} = 0.67 ^{\scriptscriptstyle+ 0.03
}_{\scriptscriptstyle- 0.03 }$ $(68\%)$, consistent with previous CFHTLenS
analysis but in tension with Planck. Adding neutrino mass as a free parameter
we are able to constrain $\sum m_\nu < 4.6\mathrm{eV}$ (95%) using CFHTLenS
data alone. Including a linear redshift dependent photo-$z$ bias $\Delta z =
p_2(z - p_1)$, we find $p_1=-0.25 ^{\scriptscriptstyle+ 0.53
}_{\scriptscriptstyle- 0.60 }$ and $p_2 = -0.15 ^{\scriptscriptstyle+ 0.17
}_{\scriptscriptstyle- 0.15 }$, and tension with Planck is only alleviated
under very conservative prior assumptions. Neither the non-minimal neutrino
mass or photo-$z$ bias models are significantly preferred by the CFHTLenS
(2-bin tomography) data.
