Bayesian inference of cosmic density fields from non-linear,
  scale-dependent, and stochastic biased tracers
  We present a Bayesian reconstruction algorithm to generate unbiased samples
of the underlying dark matter field from halo catalogues. Our new contribution
consists of implementing a non-Poisson likelihood including a deterministic
non-linear and scale-dependent bias. In particular we present the Hamiltonian
equations of motions for the negative binomial (NB) probability distribution
function. This permits us to efficiently sample the posterior distribution
function of density fields given a sample of galaxies using the Hamiltonian
Monte Carlo technique implemented in the Argo code. We have tested our
algorithm with the Bolshoi $N$-body simulation at redshift $z = 0$, inferring
the underlying dark matter density field from sub-samples of the halo catalogue
with biases smaller and larger than one. Our method shows that we can draw
closely unbiased samples (compatible within 1-$\sigma$) from the posterior
distribution up to scales of about $k$~1 h/Mpc in terms of power-spectra and
cell-to-cell correlations. We find that a Poisson likelihood yields
reconstructions with power spectra deviating more than 10% at $k$=0.2 h/Mpc.
Our reconstruction algorithm is especially suited for emission line galaxy data
for which a complex non-linear stochastic biasing treatment beyond Poissonity
becomes indispensable.
