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We apply two Bayesian hierarchical inference schemes to infer shear powerspectra, shear maps and cosmological parameters from the CFHTLenS weak lensingsurvey - the first application of this method to data. In the first approach,we sample the joint posterior distribution of the shear maps and power spectraby Gibbs sampling, with minimal model assumptions. In the second approach, wesample the joint posterior of the shear maps and cosmological parameters,providing a new, accurate and principled approach to cosmological parameterinference from cosmic shear data. As a first demonstration on data we perform a2-bin tomographic analysis to constrain cosmological parameters and investigatethe possibility of photometric redshift bias in the CFHTLenS data. Under thebaseline $\Lambda$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 CFHTLenSanalysis but in tension with Planck. Adding neutrino mass as a free parameterwe are able to constrain $\sum m_\nu < 4.6\mathrm{eV}$ (95%) using CFHTLenSdata 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 alleviatedunder very conservative prior assumptions. Neither the non-minimal neutrinomass or photo-$z$ bias models are significantly preferred by the CFHTLenS(2-bin tomography) data.

Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference