LOCAL NON-GAUSSIANITY IN THE COSMIC MICROWAVE BACKGROUND THE BAYESIAN WAY

Journal Article · Wed Dec 01 00:00:00 EST 2010 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/724/2/1262· OSTI ID:21474494

Elsner, Franz ^[1]

---

1. Max-Planck-Institut fuer Astrophysik, Karl-Schwarzschild-Strasse 1, 85748 Garching (Germany)

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{sub 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{sub NL}. Although computationally expensive, this approach allows us to construct exactly 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{sub 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.

• OSTI ID: 21474494
• Journal Information: Astrophysical Journal, Vol. 724, Issue 2; Other Information: DOI: 10.1088/0004-637X/724/2/1262; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
BACKGROUND RADIATION
COSMOLOGICAL MODELS
DATA ANALYSIS
HAMILTONIANS
MONTE CARLO METHOD
PERTURBATION THEORY
PROBABILITY
RELICT RADIATION
CALCULATION METHODS
ELECTROMAGNETIC RADIATION
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MICROWAVE RADIATION
QUANTUM OPERATORS
RADIATIONS