Determining the GRB (Redshift, Luminosity)-Distribution Using Burst Variability

We use the possible Cepheid-like luminosity estimator for the long-duration gamma-ray bursts (GRBs) developed by Reichart et al. (2000) to estimate the intrinsic luminosity, and thus the redshift, of 907 long-duration GRBs from the BATSE 4B catalog. We describe a method based on Bayesian inference which allows us to infer the intrinsic GRB burst rate as a function of redshift for bursts with estimated intrinsic luminosities and redshifts. We apply this method to the above sample of long-duration GRBs, and present some preliminary results.