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)
