Hierarchical Bayesian Inference on the intrinsic event rate of Type I gamma-ray bursts from the {\it Fermi}/GBM catalogue
Abstract
The intrinsic event-rate of Type I gamma-ray bursts (GRBs) as a function of redshift, provides a probe for binary neutron star (BNS) mergers population. However, the above-mentioned 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 {\it Fermi}/GBM Type I GRB catalogue 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 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 function of redshift is constrained up to z=5, which a local rate density of R0 = 22.6+15.0−10.6 Gpc−3 yr−1,, which is consistent with the latest gravitational-wave measurements.
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BibTeX
@misc{tianyong2026hierarchical,
title = {{Hierarchical Bayesian Inference on the intrinsic event rate of Type I gamma-ray bursts from the \it Fermi/GBM catalogue}},
author = {Cao Tian-Yong and Yi Shu-Xu and Du Yun-Fei and Yorgancioglu S. Emre and Xiong Shao-Lin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35994},
eprint = {2609.35994},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35994},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hierarchical Bayesian Inference on the intrinsic event rate of Type I gamma-ray bursts from the {\it Fermi}/GBM catalogue
AU - Cao Tian-Yong
AU - Yi Shu-Xu
AU - Du Yun-Fei
AU - Yorgancioglu S. Emre
AU - Xiong Shao-Lin
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35994
UR - https://arxiv.org/abs/2609.35994
AB - The intrinsic event-rate of Type I gamma-ray bursts (GRBs) as a function of redshift, provides a probe for binary neutron star (BNS) mergers population. However, the above-mentioned 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 {\it Fermi}/GBM Type I GRB catalogue 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 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 function of redshift is constrained up to z=5, which a local rate density of R_0 = 22.6^+15.0_−10.6 Gpc^−3 yr^−1,, which is consistent with the latest gravitational-wave measurements.
ER -