Abstract
In this paper we extend the previously published DALI-approximation for likelihoods to cases in which the parameter dependence 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/.
Author
Sellentin, Elena
Journal
Monthly Notices of the Royal Astronomical Society
Paper Publication Date
October 2015
Paper Type
Astrostatistics