  We present BAM: a novel Bias Assignment Method envisaged to generate mock
catalogs. Combining the statistics of dark matter tracers from a high
resolution cosmological $N$-body simulation and the dark matter density field
calculated from down-sampled initial conditions using efficient structure
formation solvers, we extract the halo-bias relation on a mesh of a $3\,h^{-1}$
Mpc cell side resolution as a function of properties of the dark matter density
field (e.g. local density, cosmic web type), automatically including
stochastic, deterministic, local and non-local components. We use this
information to sample the halo density field, accounting for ignored
dependencies through an iterative process. By construction, our approach
reaches $\sim 1\%$ accuracy in the majority of the $k$-range up to the Nyquist
frequency without systematic deviations for power spectra (about $k \sim 1\, h$
Mpc$^{-1}$) using either particle mesh or Lagrangian perturbation theory based
solvers. When using phase-space mapping to compensate the low resolution of the
approximate gravity solvers, our method reproduces the bispectra of the
reference within $10\%$ precision studying configurations tracing the
quasi-nonlinear regime. BAM has the potential to become a standard technique to
produce mock halo and galaxy catalogs for future galaxy surveys and
cosmological studies being highly accurate, efficient and parameter free.
