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Back to Normal! Gaussianizing posterior distributions for cosmological probes

Published online by Cambridge University Press:  01 July 2015

Robert L. Schuhmann ,
Benjamin Joachimi  and
Hiranya V. Peiris
Robert L. Schuhmann
Affiliation:
Dept. of Physics and Astronomy, University College London, Gower Place, London, UKWCE1 6BT email: [email protected]
Benjamin Joachimi
Affiliation:
Dept. of Physics and Astronomy, University College London, Gower Place, London, UKWCE1 6BT email: [email protected]
Hiranya V. Peiris
Affiliation:
Dept. of Physics and Astronomy, University College London, Gower Place, London, UKWCE1 6BT email: [email protected]
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Abstract

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We present a method to map multivariate non-Gaussian posterior probability densities into Gaussian ones via nonlinear Box-Cox transformations, and generalizations thereof. This is analogous to the search for normal parameters in the CMB, but can in principle be applied to any probability density that is continuous and unimodal. The search for the optimally Gaussianizing transformation amongst the Box-Cox family is performed via a maximum likelihood formalism. We can judge the quality of the found transformation a posteriori: qualitatively via statistical tests of Gaussianity, and more illustratively by how well it reproduces the credible regions. The method permits an analytical reconstruction of the posterior from a sample, e.g. a Markov chain, and simplifies the subsequent joint analysis with other experiments. Furthermore, it permits the characterization of a non-Gaussian posterior in a compact and efficient way. The expression for the non-Gaussian posterior can be employed to find analytic formulae for the Bayesian evidence, and consequently be used for model comparison.

Keywords

methods: data analysismethods: numericalcosmology: observations
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 10 , Symposium S306: Statistical Challenges in 21st Century Cosmology , May 2014 , pp. 13 - 15
Copyright
Copyright © International Astronomical Union 2015 

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