  We have tested several models of GRB luminosity and redshift distribution
functions for compatibility with the BATSE 4B number versus peak flux relation.
Our results disagree with recent claims that current GRB observations can be
used to strongly constrain the cosmic star formation history. Instead, we find
that relaxing the assumption that GRBs are standard candles renders a very
broad range of models consistent with the BATSE number-flux relation. We
explicitly construct two sample distributions, one tracing the star formation
history and one with a constant comoving density. We show that both
distributions are compatible with the observed fluxes and redshifts of the
bursts GRB970508, GRB971214, and GRB980703, and we discuss the measurements
required to distinguish the two models.
