  On large scales, the higher order moments of the mass distribution,
$S_J=\xibar_J/\xibar_2^{J-1}$, e.g., the skewness $S_3$ and kurtosis $S_4$, can
be predicted using non-linear perturbation theory. Comparison of these
predictions with moments of the observed galaxy distribution probes the bias
between galaxies and mass. Applying this method to models with initially
Gaussian fluctuations and power spectra $P(k)$ similar to that of galaxies in
the APM survey, we find that the predicted higher order moments $S_J(R)$ are in
good agreement with those directly inferred from the APM survey {\it in the
absence of bias}. We use this result to place limits on the linear and
non-linear bias parameters. Models in which the extra power observed on large
scales (with respect to standard CDM) is produced by scale-dependent bias match
the APM higher order amplitudes only if non-linear bias (rather than non-linear
gravity) generates the observed higher order moments. When normalized to COBE
DMR, these models are significantly ruled out by the $S_3$ observations. The
cold plus hot dark matter model normalized to COBE can reproduce the APM higher
order correlations if one introduces non-linear bias terms, while the
low-density CDM model with a cosmological constant does not require any bias to
fit the large-scale amplitudes.
