  The statistics of large-scale structure in the Universe can be used to probe
non-Gaussianity of the primordial density field, complementary to existing
constraints from the cosmic microwave background. In particular, the scale
dependence of halo bias, which affects the halo distribution at large scales,
represents a promising tool for analyzing primordial non-Gaussianity of local
form. Future observations, for example, may be able to constrain the
trispectrum parameter gNL that is difficult to study and constrain using the
CMB alone. We investigate how galaxy and matter bispectra can distinguish
between the two non-Gaussian parameters fNL and gNL, whose effects give nearly
degenerate contributions to the power spectra. We use a generalization of the
univariate bias approach, making the hypothesis that the number density of
halos forming at a given position is a function of the local matter density
contrast and of its local higher-order statistics. Using this approach, we
calculate the halo-matter bispectra and analyze their properties. We determine
a connection between the sign of the halo bispectrum on large scales and the
parameter gNL. We also construct a combination of halo and matter bispectra
that is sensitive to fNL, with little contamination from gNL. We study both the
case of single and multiple sources to the primordial gravitational potential,
discussing how to extend the concept of stochastic halo bias to the case of
bispectra. We use a specific halo mass-function to calculate numerically the
bispectra in appropriate squeezed limits, confirming our theoretical findings.
