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

TL;DR

This paper presents an exact Bayesian method for detecting local non-Gaussianity in CMB data, offering a full posterior distribution approach that complements traditional estimators and is relevant for upcoming high-precision measurements.

Contribution

The paper introduces a Bayesian framework with Hamiltonian Monte Carlo sampling for analyzing non-Gaussianity in CMB data, providing a more complete statistical characterization.

Findings

Bayesian method yields consistent results with Gaussian maps.

Error bars on f_nl do not increase for non-Gaussian maps in Bayesian analysis.

Approach is computationally intensive but offers exact posterior distributions.

Abstract

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.