A Frequentist-Bayesian approach to estimating the unknown redshifts of BATSE catalog Gamma-Ray Bursts

We present a catalog of probability density functions and estimates for the unknown redshifts of individual BATSE Gamma-Ray Bursts (GRBs). This result is based on careful selection, classification, and modeling of the population distribution of BATSE GRBs in the 5-dimensional space of redshift and the four intrinsic prompt-emission properties: the isotropic 1024ms peak luminosity, the total isotropic emission, the spectral peak energy, and the intrinsic duration, while taking into account the complex detection threhold of BATSE and potential sample incompleteness. Our modeling approach enables us to constrain the redshifts of BATSE GRBs to average uncertainty ranges of <0.7 and <1.7 with 50% and 90% probabilities respectively. We compare our predictions with the previous independent estimates of BATSE GRB redshifts and find that all previous independent reports are completely inconsistent with each other and with our predictions. We further provide plausible explanations for the observed inconsistencies in the previous estimates. The presented catalog here can be useful for demographic studies of short- and long-duration GRBs and the methodology can be adapted for studying other GRB datasets, such as Fermi and Neil Gehrels' Swift GRB catalogs.