Bayesian non-linear large-scale structure inference of the Sloan Digital Sky Survey Data Release 7

In this work, we present the first non-linear, non-Gaussian full Bayesian large-scale structure analysis of the cosmic density field conducted so far. The density inference is based on the Sloan Digital Sky Survey (SDSS) Data Release 7, which covers the northern galactic cap. We employ a novel Bayesian sampling algorithm, which enables us to explore the extremely high dimensional non-Gaussian, non-linear lognormal Poissonian posterior of the three-dimensional density field conditional on the data. These techniques are efficiently implemented in the Hamiltonian Density Estimation and Sampling (HADES) computer algorithm and permit the precise recovery of poorly sampled objects and non-linear density fields. The non-linear density inference is performed on a 750-Mpc cube with roughly 3-Mpc grid resolution, while accounting for systematic effects, introduced by survey geometry and selection function of the SDSS, and the correct treatment of a Poissonian shot noise contribution. Our high-resolution results represent remarkably well the cosmic web structure of the cosmic density field. Filaments, voids and clusters are clearly visible. Further, we also conduct a dynamical web classification and estimate the web-type posterior distribution conditional on the SDSS data.