  In this work we present a new and efficient Bayesian method for nonlinear
three dimensional large scale structure inference. We employ a Hamiltonian
Monte Carlo (HMC) sampler to obtain samples from a multivariate highly
non-Gaussian lognormal Poissonian density posterior given a set of
observations. The HMC allows us to take into account the nonlinear relations
between the observations and the underlying density field which we seek to
recover. As the HMC provides a sampled representation of the density posterior
any desired statistical summary, such as the mean, mode or variance, can be
calculated from the set of samples. Further, it permits us to seamlessly
propagate non-Gaussian uncertainty information to any final quantity inferred
from the set of samples. The developed method is extensively tested in a
variety of test scenarios, taking into account a highly structured survey
geometry and selection effects. Tests with a mock galaxy catalog based on the
millennium run show that the method is able to recover the filamentary
structure of the nonlinear density field. The results further demonstrate the
feasibility of non-Gaussian sampling in high dimensional spaces, as required
for precision nonlinear large scale structure inference. The HMC is a flexible
and efficient method, which permits for simple extension and incorporation of
additional observational constraints. Thus, the method presented here provides
an efficient and flexible basis for future high precision large scale structure
inference.
