  We present a novel approach to the construction of mock galaxy catalogues for
large-scale structure analysis based on the distribution of dark matter halos
obtained with effective bias models at the field level. We aim to produce mock
galaxy catalogues capable of generating accurate covariance matrices for a
number of cosmological probes that are expected to be measured in current and
forthcoming galaxy redshift surveys (e.g. two- and three-point statistics). We
use the bias assignment method (BAM) to model the statistics of halo
distribution through a learning algorithm using a few detailed $N$-body
simulations, and approximated gravity solvers based on Lagrangian perturbation
theory. Using specific models of halo occupation distributions, we generate
galaxy mocks with the expected number density and central-satellite fraction of
emission-line galaxies, which are a key target of the DESI experiment. BAM
generates mock catalogues with per cent accuracy in a number of summary
statistics, such as the abundance, the two- and three-point statistics of halo
distributions, both in real and redshift space. In particular, the mock galaxy
catalogues display $\sim 3\%-10\%$ accuracy in the multipoles of the power
spectrum up to scales of $k\sim 0.4\,h^{-1}{\rm Mpc}$. We show that covariance
matrices of two- and three-point statistics obtained with BAM display a similar
structure to the reference simulation. BAM offers an efficient way to produce
mock halo catalogues with accurate two- and three-point statistics, and is able
to generate a variety of multi-tracer catalogues with precise covariance
matrices of several cosmological probes. We discuss future developments of the
algorithm towards mock production in DESI and other galaxy-redshift surveys.
(Abridged)
