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.
