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Peer-reviewedCC BY 4.0The Astrophysical Journal

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

  • Tian-Yong Cao1,2
  • Shu-Xu Yi1,2
  • Yun-Fei Du1,2,3
  • Emre S. Yorgancioglu1,2
  • Shao-Lin Xiong1,2
  1. 1Chinese Academy of Sciences
  2. 2University of Chinese Academy of Sciences
  3. 3Beijing Academy Science and Technology Branch
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@article{cao2026hierarchical,
  title = {{Hierarchical Bayesian Inference on the Intrinsic Event Rate of Type I Gamma-Ray Bursts from the Fermi/GBM Catalog}},
  author = {Tian-Yong Cao and Shu-Xu Yi and Yun-Fei Du and Emre S. Yorgancioglu and Shao-Lin Xiong},
  journal = {The Astrophysical Journal},
  year = {2026},
  month = oct,
  doi = {10.3847/1538-4357/aeaa3f},
  url = {https://iopscience.iop.org/article/10.3847/1538-4357/aeaa3f},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Hierarchical Bayesian Inference on the Intrinsic Event Rate of Type I Gamma-Ray Bursts from the Fermi/GBM Catalog
AU  - Tian-Yong Cao
AU  - Shu-Xu Yi
AU  - Yun-Fei Du
AU  - Emre S. Yorgancioglu
AU  - Shao-Lin Xiong
PY  - 2026
DA  - 2026/10/26
JO  - The Astrophysical Journal
DO  - 10.3847/1538-4357/aeaa3f
UR  - https://iopscience.iop.org/article/10.3847/1538-4357/aeaa3f
AB  - 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.
SN  - 0004-637X
SN  - 1538-4357
ER  -