  Fisher Information Matrix methods are commonly used in cosmology to estimate
the accuracy that cosmological parameters can be measured with a given
experiment, and to optimise the design of experiments. However, the standard
approach usually assumes both data and parameter estimates are
Gaussian-distributed. Further, for survey forecasts and optimisation it is
usually assumed the power-spectra covariance matrix is diagonal in
Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will
tend to correlate small-scale power, moving information from lower to
higher-order moments of the field. This movement of information will change the
predictions of cosmological parameter accuracy. In this paper we quantify this
loss of information by comparing naive Gaussian Fisher matrix forecasts with a
Maximum Likelihood parameter estimation analysis of a suite of mock weak
lensing catalogues derived from N-body simulations, based on the SUNGLASS
pipeline, for a 2-D and tomographic shear analysis of a Euclid-like survey. In
both cases we find that the 68% confidence area of the Omega_m-sigma_8 plane
increases by a factor 5. However, the marginal errors increase by just 20 to
40%. We propose a new method to model the effects of nonlinear shear-power
mode-coupling in the Fisher Matrix by approximating the shear-power
distribution as a multivariate Gaussian with a covariance matrix derived from
the mock weak lensing survey. We find that this approximation can reproduce the
68% confidence regions of the full Maximum Likelihood analysis in the
Omega_m-sigma_8 plane to high accuracy for both 2-D and tomographic weak
lensing surveys. Finally, we perform a multi-parameter analysis of Omega_m,
sigma_8, h, n_s, w_0 and w_a to compare the Gaussian and non-linear
mode-coupled Fisher matrix contours. (Abridged)
