A fast, always positive definite and normalizable approximation of non-Gaussian likelihoods

作者：Sellentin Elena^*

来源：Monthly Notices of the Royal Astronomical Society, 2015, 453(1): 893-898.

DOI：10.1093/mnras/stv1671

• methods: analytical
• methods: data analysis
• methods: numerical
• methods: statistical

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/.

• 出版日期2015-10-11