  If gamma-ray bursts (GRBs) are cosmological they need not necessarily be
spatially coincident with a host galaxy--in many cosmological models the
progenitors are ejected to large distances from their parent galaxies. While
the optical transient of GRB 970228 may be close to a faint galaxy, there are
several other galaxies in the field which could be the host if the progenitors
are ejected to ~50 kpc. If GRBs come from such a widely distributed progenitor
population then it should be possible to search for a statistical correlation
between optical transients and nearby galaxies. We provide a statistical
framework for quantifying a correlation between potential host galaxies and
GRBs, taking into account that galaxies are clustered. From simulations, we
estimate that if GRBs occur within l < 100 kpc of their host, then optical
observations B < 24.0 of the galaxy field near just 6 optical transient
positions are required to find a correlation with potential hosts at the 95
percent confidence level. The methodology constructed herein is extendible to
any cross-correlation analysis and is especially useful if either set of
objects is clustered. Ultimately, if the distance scale to GRBs is established
as cosmological, this analysis can be used to determine the spatial
distribution of GRBs near their host galaxies.
