  We present a comparison between approximated methods for the construction of
mock catalogs based on the halo-bias mapping technique. To this end, we use as
reference a high resolution $N$-body simulation of 3840$^3$ dark matter
particles on a 400$h^{-1}\rm{Mpc}$ cube box from the Multidark suite. In
particular, we explore parametric versus non-parametric bias mapping approaches
and compare them at reproducing the halo distribution in terms of the two and
three point statistics down to $\sim 10^8\,{\rm M}_{\odot}\,h^{-1}$ halo
masses. Our findings demonstrate that the parametric approach remains
inaccurate even including complex deterministic and stochastic components. On
the contrary, the non-parametric one is indistinguishable from the reference
$N$-body calculation in the power-spectrum beyond $k=1\,h\,{\rm Mpc}^{-1}$, and
in the bispectrum for typical configurations relevant to baryon acoustic
oscillation analysis. We conclude, that approaches which extract the full bias
information from $N$-body simulations in a non-parametric fashion are ready for
the analysis of the new generation of large scale structure surveys.
