Sebastian Dorn, Niels Oppermann, Rishi Khatri, Marco Selig, Torsten A. Enß lin
We present an approximate calculation of the full Bayesian posterior probability distribution for the local non-Gaussianity parameter f_nl from observations of Cosmic Microwave Background anisotropies within the framework of information field theory. The approximation that we introduce allows us to dispense with numerically expensive sampling techniques. We use a novel posterior validation method (DIP-test) in cosmology to test the precision of our method. It transfers inaccuracies of the calculated posterior into deviations from a uniform distribution for a specially constructed test quantity. For this procedure we study toy-cases that use one- and two-dimensional flat skies, as well as the full spherical sky. We find that we are able to calculate the posterior precisely under a flat-sky approximation, albeit not in the spherical case. We argue that this is most likely due to an insufficient precision of the used numerical implementation of the spherical harmonic transform, which might affect other non-Gaussianity estimators as well. Furthermore, we present how a non-linear reconstruction of the primordial gravitational potential on the full spherical sky can be obtained in principle. Using the flat-sky approximation, we find deviations for the posterior of f_nl from a Gaussian shape that become more significant for larger values of the underlying true f_nl. We also perform a comparison to the well-known estimator of Komatsu et al. (2005) and finally derive the posterior for the local non-Gaussianity parameter g_nl as an example of how to extend the introduced formalism to higher orders of non-Gaussianity.
View original:
http://arxiv.org/abs/1307.3884
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