Likelihood of the Power Spectrum in Cosmological Parameter Estimation
  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.
