  We show that current surveys have at least as much signal to noise in
higher-order statistics as in the power spectrum at weakly nonlinear scales. We
discuss how one can use this information to determine the mean of the galaxy
halo occupation distribution (HOD) using only large-scale information, through
galaxy bias parameters determined from the galaxy bispectrum and trispectrum.
After introducing an averaged, reasonably fast to evaluate, trispectrum
estimator, we show that the expected errors on linear and quadratic bias
parameters can be reduced by at least 20-40%. Also, the inclusion of the
trispectrum information, which is sensitive to "three-dimensionality" of
structures, helps significantly in constraining the mass dependence of the HOD
mean. Our approach depends only on adequate modeling of the abundance and
large-scale clustering of halos and thus is independent of details of how
galaxies are distributed within halos. This provides a consistency check on the
traditional approach of using two-point statistics down to small scales, which
necessarily makes more assumptions. We present a detailed forecast of how well
our approach can be carried out in the case of the SDSS.
