Likelihood of the Power Spectrum in Cosmological Parameter Estimation

TL;DR

This paper investigates the impact of different likelihood approximations on cosmological parameter estimation from galaxy power spectra, highlighting biases and proposing better likelihood models.

Contribution

It demonstrates that Gaussian likelihoods can bias parameter estimates and shows that Gaussian plus log-normal likelihoods improve accuracy in cosmological analyses.

Findings

Gaussian likelihoods can significantly bias f_NL estimates.

Gaussian plus log-normal likelihoods outperform pure Gaussian models.

Exact likelihoods may still lead to biased parameters.

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.