A fast, always positive definite and normalizable approximation of
  non-Gaussian likelihoods
  In this paper we extent the previously published DALI-approximation for
likelihoods to cases in which the parameter dependency is in the covariance
matrix. The approximation recovers non-Gaussian likelihoods, and reduces to the
Fisher matrix approach in the case of Gaussianity. It works with the minimal
assumptions of having Gaussian errors on the data, and a covariance matrix that
possesses a converging Taylor approximation. The resulting approximation works
in cases of severe parameter degeneracies and in cases where the Fisher matrix
is singular. It is at least $1000$ times faster than a typical Monte Carlo
Markov Chain run over the same parameter space. Two example applications, to
cases of extremely non-Gaussian likelihoods, are presented -- one demonstrates
how the method succeeds in reconstructing completely a ring-shaped likelihood.
A public code is released here: http://lnasellentin.github.io/DALI/
