  We present the new method DALI (Derivative Approximation for LIkelihoods) for
reconstructing and forecasting posteriors. DALI extends the Fisher Matrix
formalism but allows for a much wider range of posterior shapes. While the
Fisher Matrix formalism is limited to yield ellipsoidal confidence contours,
our method can reproduce the often observed flexed, deformed or curved shapes
of known posteriors. This gain in shape fidelity is obtained by expanding the
posterior to higher order in derivatives with respect to parameters, such that
non-Gaussianity in the parameter space is taken into account. The resulting
expansion is positive definite and normalizable at every order. Here, we
present the new technique, highlight its advantages and limitations, and show a
representative application to a posterior of dark energy parameters from
supernovae measurements.
