Local non-Gaussianity in the Cosmic Microwave Background the Bayesian way

Franz Elsner, Benjamin D. Wandelt

Published 2010-10-06Version 1

We introduce an exact Bayesian approach to search for non-Gaussianity of local type in Cosmic Microwave Background (CMB) radiation data. Using simulated CMB temperature maps, the newly developed technique is compared against the conventional frequentist bispectrum estimator. Starting from the joint probability distribution, we obtain analytic expressions for the conditional probabilities of the primordial perturbations given the data, and for the level of non-Gaussianity, f_nl, given the data and the perturbations. We propose Hamiltonian Monte Carlo sampling as a means to derive realizations of the primordial fluctuations from which we in turn sample f_nl. Although being computationally expensive, this approach allows us to exactly construct the full target posterior probability distribution. When compared to the frequentist estimator, applying the Bayesian method to Gaussian CMB maps provides consistent results. For the analysis of non-Gaussian maps, however, the error bars on f_nl do not show excess variance within the Bayesian framework. This finding is of particular relevance in the light of upcoming high precision CMB measurements obtained by the Planck satellite mission.