The wide-area imaging surveys with the Herschel Space Observatory at
submillimeter (sub-mm) wavelengths have now resulted in catalogs of the
order of one-hundred-thousand dusty, starburst galaxies. These galaxies
capture an important phase of galaxy formation and evolution, but,
unfortunately, the redshift distribution of these galaxies, N(z), is
still mostly uncertain due to limitations associated with counterpart
identification at optical wavelengths and spectroscopic follow-up. We
make a statistical estimate of N(z) using a clustering analysis of
sub-mm galaxies detected at each of 250, 350 and 500 μm from the
Herschel Multi-tiered Extragalactic Survey centered on the Boötes
field. We cross-correlate Herschel galaxies against galaxy samples at
optical and near-IR wavelengths from the Sloan Digital Sky Survey, the
NOAO Deep Wide Field Survey, and the Spitzer Deep Wide Field Survey. We
create optical and near-IR galaxy samples based on their photometric or
spectroscopic redshift distributions and test the accuracy of those
redshift distributions with similar galaxy samples defined with catalogs
from the Cosmological Evolution Survey (COSMOS), which has superior
spectroscopic coverage. We model the clustering auto- and
cross-correlations of Herschel and optical/IR galaxy samples to estimate
N(z) and clustering bias factors. The S 350 > 20 mJy
galaxies have a bias factor varying with redshift as b(z) =
1.0+1.0 - 0.5(1 + z)1.2+0.3 -
0.7 . This bias and the redshift dependence is broadly in
agreement with galaxies that occupy dark matter halos of mass in the
range of 1012 to 1013 M ⊙. We find
that galaxy selections in all three Spectral and Photometric Imaging
Receiver (SPIRE) bands share a similar average redshift, with langzrang
= 1.8 ± 0.2 for 250 μm selected samples, and langzrang = 1.9
± 0.2 for both 350 and 500 μm samples, while their
distributions behave differently. For 250 μm selected galaxies we
find the a larger number of sources with z