Cosmological parameter inference from galaxy clustering: the effect of the posterior distribution of the power spectrum

We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the posterior distribution P_R we expect for a Gaussian density field delta_k, even if we vary the covariance matrix according to the model to be tested. We compare alternative posterior distributions with P_R, both mode-by-mode and in terms of expected f_NL-measurements. Marginalising over a Gaussian posterior distribution P_f with fixed covariance matrix yields a posterior mean value of f_NL which, for a data set with the characteristics of Euclid, will be underestimated by Delta f_NL=0.4, while for the data release 9 (DR9) of the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) it will be underestimated by Delta f_NL=19.1. The inverse cubic normal distribution (P_ICN) agrees very well with P_R at all scales and for all data sets, hence providing the same marginalised value. Adopting this likelihood function means that we do not require a different covariance matrix for each model to be tested: this dependence is absorbed into the functional form of the posterior. Thus, the computational burden of analysis is significantly reduced.