  Analysis of three-dimensional cosmological surveys has the potential to
answer outstanding questions on the initial conditions from which structure
appeared, and therefore on the very high energy physics at play in the early
Universe. We report on recently proposed statistical data analysis methods
designed to study the primordial large-scale structure via physical inference
of the initial conditions in a fully Bayesian framework, and applications to
the Sloan Digital Sky Survey data release 7. We illustrate how this approach
led to a detailed characterization of the dynamic cosmic web underlying the
observed galaxy distribution, based on the tidal environment.
