Likelihood of the Power Spectrum in Cosmological Parameter Estimation

Abstract

The likelihood function is a crucial element of parameter estimation. In analyses of galaxy overdensities and weak lensing shear, one often approximates the likelihood of the power spectrum with a Gaussian distribution. The posterior probability derived from such a likelihood deviates considerably from the exact posterior on the largest scales probed by any survey, where the central limit theorem does not apply. We show that various forms of Gaussian likelihoods can have a significant impact on the estimation of the primordial non-Gaussianity parameter f_NL from the galaxy angular power spectrum. The Gaussian plus log-normal likelihood, which has been applied successfully in analyses of the cosmic microwave background, outperforms the Gaussian likelihoods. Nevertheless, even if the exact likelihood of the power spectrum is used, the estimated parameters may be still biased. As such, the likelihoods and estimators need to be thoroughly examined for potential systematic errors.

6 pages, 4 figures; accepted for publication in ApJ

References in corpus (12)

• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• Cosmological Constraints from the SDSS Luminous Red Galaxies
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• On the Robustness of the Acoustic Scale in the Low-Redshift Clustering of Matter
• CFHTLenS: Combined probe cosmological model comparison using 2D weak gravitational lensing
• COSMOS: 3D weak lensing and the growth of structure
• Cosmic shear results from the deep lens survey - I: Joint constraints on omega_m and sigma_8 with a two-dimensional analysis
• On the assumption of Gaussianity for cosmological two-point statistics and parameter dependent covariance matrices
• Cosmic tomographies: baryon acoustic oscillations and weak lensing
• Effect of model-dependent covariance matrix for studying Baryon Acoustic Oscillations
• A quasi-Gaussian approximation for the probability distribution of correlation functions

Cited by in corpus (7)

• Gaussian covariance matrices for anisotropic galaxy clustering measurements
• Cosmological Inference from Galaxy-Clustering Power Spectrum: Gaussianization and Covariance Decomposition
• Accurate halo-galaxy mocks from automatic bias estimation and particle mesh gravity solvers
• Exact joint likelihood of pseudo-$C_{\ell }$ estimates from correlated Gaussian cosmological fields
• A quasi-Gaussian approximation for the probability distribution of correlation functions
• Reconstructing the Cosmic Expansion History with a Monotonicity Prior
• Constrained correlation functions from the Millennium Simulation