  We show how the peak-background split can be generalized to predict the
effect of non-local primordial non-Gaussianity on the clustering of halos. Our
approach is applicable to arbitrary primordial bispectra. We show that the
scale-dependence of halo clustering predicted in the peak-background split
(PBS) agrees with that of the local-biasing model on large scales. On smaller
scales, k >~ 0.01 h/Mpc, the predictions diverge, a consequence of the
assumption of separation of scales in the peak-background split. Even on large
scales, PBS and local biasing do not generally agree on the amplitude of the
effect outside of the high-peak limit. The scale dependence of the biasing -
the effect that provides strong constraints to the local-model bispectrum - is
far weaker for the equilateral and self-ordering-scalar-field models of
non-Gaussianity. The bias scale dependence for the orthogonal and folded models
is weaker than in the local model (~ 1/k), but likely still strong enough to be
constraining. We show that departures from scale-invariance of the primordial
power spectrum may lead to order-unity corrections, relative to predictions
made assuming scale-invariance - to the non-Gaussian bias in some of these
non-local models for non-Gaussianity. An Appendix shows that a non-local model
can produce the local-model bispectrum, a mathematical curiosity we uncovered
in the course of this investigation.
