Bayesian Analysis of Cosmic Structures

Abstract

We revise the Bayesian inference steps required to analyse the cosmological large-scale structure. Here we place special emphasis on the complications which arise due to the non-Gaussian character of the Galaxy and matter distribution. In particular, we investigate the advantages and limitations of the Poisson-lognormal model and discuss how to extend this work. With the lognormal prior using the Hamiltonian sampling technique and on scales of about 4 h^{− 1} Mpc we find that the over-dense regions are very well reconstructed; however, the under-dense regions (void statistics) are quantitatively poorly recovered. Contrary to the maximum a posteriori (MAP), a solution which was shown to over-estimate the density in under-dense regions, we obtain lower densities than in N-body simulations. This is due to the fact that the MAP solution is conservative, whereas the full posterior yields samples which are consistent with the prior statistics. The lognormal prior is not able to capture the full non-linear regime at scales below ∼ 10 h^{− 1} Mpc for which higher-order correlations would be required to describe the matter statistics. However, we confirm, as was recently shown in the context of Lyα forest tomography, that the Poisson-lognormal model provides the correct two-point statistics (or power spectrum).