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 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 log-normal Poissonian posterior of the three dimensional density field conditional on the data. These techniques are efficiently implemented in the 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 estimated the web type posterior distribution conditional on the SDSS data.Comment: 18 pages, 11 figure