Emulating the CFHTLenS Weak Lensing data: Cosmological Constraints from
  moments and Minkowski functionals
  Weak gravitational lensing is a powerful cosmological probe, with
non--Gaussian features potentially containing the majority of the information.
We examine constraints on the parameter triplet $(\Omega_m,w,\sigma_8)$ from
non-Gaussian features of the weak lensing convergence field, including a set of
moments (up to $4^{\rm th}$ order) and Minkowski functionals, using publicly
available data from the 154deg$^2$ CFHTLenS survey. We utilize a suite of
ray--tracing N-body simulations spanning 91 points in $(\Omega_m,w,\sigma_8)$
parameter space, replicating the galaxy sky positions, redshifts and shape
noise in the CFHTLenS catalogs. We then build an emulator that interpolates the
simulated descriptors as a function of $(\Omega_m,w,\sigma_8)$, and use it to
compute the likelihood function and parameter constraints. We employ a
principal component analysis to reduce dimensionality and to help stabilize the
constraints with respect to the number of bins used to construct each
statistic. Using the full set of statistics, we find
$\Sigma_8\equiv\sigma_8(\Omega_m/0.27)^{0.55}=0.75\pm0.04$ (68% C.L.), in
agreement with previous values. We find that constraints on the
$(\Omega_m,\sigma_8)$ doublet from the Minkowski functionals suffer a strong
bias. However, high-order moments break the $(\Omega_m,\sigma_8)$ degeneracy
and provide a tight constraint on these parameters with no apparent bias. The
main contribution comes from quartic moments of derivatives.
