  We develop a new test of local bias, by constructing a locally biased halo
density field from sampling the dark matter-halo distribution. Our test differs
from conventional tests in that it preserves the full scatter in the bias
relation and it does not rely on perturbation theory. We put forward that bias
parameters obtained using a smoothing scale R can only be applied to computing
the halo power spectrum at scales k ~ 1/R. Our calculations can automatically
include the running of bias parameters and give vanishingly small loop
corrections at low-k. Our proposal results in much better agreement of the
sampling and perturbation theory results with simulations. In particular,
unlike the standard interpretation of local bias in the literature, our
treatment of local bias does not generate a constant power in the low-k limit.
We search for extra noise in the Poisson corrected halo power spectrum at
wavenumbers below its turn-over and find no evidence of significant positive
noise (as predicted by the standard interpretation) while we find evidence of
negative noise coming from halo exclusion for very massive halos. Using
perturbation theory and our non-perturbative sampling technique we also
demonstrate that nonlocal bias effects discovered recently in simulations
impact the power spectrum only at the few percent level in the weakly nonlinear
regime.
