Determining the Gamma-Ray Burst Rate as a Function of Redshift

We exploit the 14 gamma-ray bursts (GRBs) with known redshifts $z$ and the 7 GRBs for which there are constraints on $z$ to determine the GRB rate $R_{\rm GRB}(z)$, using a method based on Bayesian inference. We find that, despite the qualitative differences between the observed GRB rate and estimates of the SFR in the universe, current data are consistent with $R_{\mathrm{G}\mathrm{R}\mathrm{B}}(z)$ being proportional to the SFR.