  We develop a general formalism for analysing parameter information from
non-Gaussian cosmic fields. The method can be adapted to include the nonlinear
effects in galaxy redshift surveys, weak lensing surveys and cosmic velocity
field surveys as part of parameter estimation. It can also be used as a test of
non-Gaussianity of the Cosmic Microwave Background. Generalising Maximum
Likelihood analysis to second-order, we calculate the nonlinear Fisher
Information matrix and likelihood surfaces in parameter space. To this order we
find that the information content is always increased by including
nonlinearity. Our methods are applied to a realistic model of a galaxy redshift
survey, including nonlinear evolution, galaxy bias, shot-noise and
redshift-space distortions to second-order. We find that including
nonlinearities allows all of the degeneracies between parameters to be lifted.
Marginalised parameter uncertainties of a few percent will then be obtainable
using forthcoming galaxy redshift surveys.
