Hierarchical Bayesian Inference on the Intrinsic Event Rate of Type I Gamma-Ray Bursts from the Fermi/GBM Catalog

The intrinsic event-rate of Type I gamma-ray bursts (GRBs) as a function of redshift, provides a probe for the binary neutron star (BNS) merger population. However, the abovementioned inference is complicated by instrumental selection effects, the lack of redshift measurements for the majority of GRBs, and uncertainties in jet geometry. In this work, we applied a hierarchical Bayesian inference framework to the Fermi/GBM Type I GRB catalog to reconstruct the underlying event-rate population. This framework accounts for the selection effects and marginalizes over the limited-information posteriors of individual GRB redshifts and jet structures. The population model uses the parameterized luminosity function, distribution of jet structure parameters, the Madau-–Dickinson star formation rate and a delay-time distribution of BNS mergers. The posterior distribution of the hyperparameters in the model are to be inferred, using a GPU-accelerated MCMC algorithm. The intrinsic event rate density as a function of redshift is constrained up to z = 5, which a local rate density of R 0 = 22 . 6 − 10.6 + 15.0 Gpc − 3 yr − 1 , which is consistent with the latest gravitational-wave measurements.