  The peak-background split argument is commonly used to relate the abundance
of dark matter halos to their spatial clustering. Testing this argument
requires an accurate determination of the halo mass function. We present a
Maximum Likelihood method for fitting parametric functional forms to halo
abundances which differs from previous work because it does not require binned
counts. Our conclusions do not depend on whether we use our method or more
conventional ones. In addition, halo abundances depend on how halos are
defined. Our conclusions do not depend on the choice of link length associated
with the friends-of-friends halo-finder, nor do they change if we identify
halos using a spherical overdensity algorithm instead. The large scale halo
bias measured from the matter-halo cross spectrum b_x and the halo
autocorrelation function b_xi (on scales k~0.03h/Mpc and r ~50 Mpc/h) can
differ by as much as 5% for halos that are significantly more massive than the
characteristic mass M*. At these large masses, the peak background split
estimate of the linear bias factor b1 is 3-5% smaller than b_xi, which is 5%
smaller than b_x. We discuss the origin of these discrepancies: deterministic
nonlinear local bias, with parameters determined by the peak-background split
argument, is unable to account for the discrepancies we see. A simple linear
but nonlocal bias model, motivated by peaks theory, may also be difficult to
reconcile with our measurements. More work on such nonlocal bias models may be
needed to understand the nature of halo bias at this level of precision.
