  If gamma-ray bursts originate in galaxies at cosmological distances, the host
galaxy should be detected if a burst error box is searched deep enough; are the
host galaxies present? We present and implement a statistical methodology which
evaluates whether the observed galaxy detections in a burst's error box are
consistent with the presence of the host galaxy, or whether all the detections
can be attributed to unrelated background galaxies. This methodology requires
the model-dependent distribution of host galaxy fluxes. While our methodology
was derived for galaxies in burst error boxes, it can be applied to other
candidate host objects (e.g., active galaxies) and to other types of error
boxes. As examples, we apply this methodology to two published studies of burst
error boxes. We find that the nine error boxes observed by Larson and McLean
(1997) are too large to discriminate between the presence or absence of host
galaxies, while the absence of bright galaxies in the four significantly
smaller error boxes observed by HST (Schaefer et al. 1997) does confirm that
there is a "no-host galaxy" problem within the "minimal" host galaxy model.
