Bayesian analysis of cosmic structures

TL;DR

This paper revises Bayesian methods for analyzing cosmic large-scale structures, emphasizing the non-Gaussian nature of galaxy distributions, and evaluates the effectiveness of the Poisson-lognormal model in reconstructing cosmic density fields.

Contribution

It demonstrates the application of Hamiltonian sampling with a lognormal prior for cosmic structure analysis and discusses the model's limitations and extensions.

Findings

Over-dense regions are well reconstructed at 4 h^{-1} Mpc scales.

Under-dense regions are poorly recovered, with lower densities than N-body simulations.

The Poisson-lognormal model accurately reproduces the two-point statistics of matter distribution.

Abstract

We revise the Bayesian inference steps required to analyse the cosmological large-scale structure. Here we make special emphasis in 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 excellent reconstructed, however, under-dense regions (void statistics) are quantitatively poorly recovered. Contrary to the maximum a posteriori (MAP) solution which was shown to over-estimate the density in the 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 it was recently shown in the context of Ly-alpha forest tomography that the Poisson-lognormal model provides the correct two-point statistics (or power-spectrum).