Non-Gaussian forecasts of weak lensing with and without priors
  Assuming a Euclid-like weak lensing data set, we compare different methods of
dealing with its inherent parameter degeneracies. Including priors into a data
analysis can mask the information content of a given data set alone. However,
since the information content of a data set is usually estimated with the
Fisher matrix, priors are added in order to enforce an approximately Gaussian
likelihood. Here, we compare priorless forecasts to more conventional forecasts
that use priors. We find strongly non-Gaussian likelihoods for 2d-weak lensing
if no priors are used, which we approximate with the DALI-expansion. Without
priors, the Fisher matrix of the 2d-weak lensing likelihood includes unphysical
values of $\Omega_m$ and $h$, since it does not capture the shape of the
likelihood well. The Cramer-Rao inequality then does not need to apply. We find
that DALI and Monte Carlo Markov Chains predict the presence of a dark energy
with high significance, whereas a Fisher forecast of the same data set also
allows decelerated expansion. We also find that a 2d-weak lensing analysis
provides a sharp lower limit on the Hubble constant of $h > 0.4$, even if the
equation of state of dark energy is jointly constrained by the data. This is
not predicted by the Fisher matrix and usually masked in other works by a sharp
prior on $h$. Additionally, we find that DALI estimates Figures of Merit in the
presence of non-Gaussianities better than the Fisher matrix. We additionally
demonstrate how DALI allows switching to a Hamiltonian Monte Carlo sampling of
a highly curved likelihood with acceptance rates of $\approx 0.5$, an effective
covering of the parameter space, and numerically effectively costless leapfrog
steps. This shows how quick forecasts can be upgraded to accurate forecasts
whenever needed. Results were gained with the public code from
http://lnasellentin.github.io/DALI/
