Hierarchical Population Inference with Normalizing Flows for Binary Black Holes
Abstract
Low-dimensional parametric mass models are standard in gravitational-wave population inference, but their rigidity can bias the recovered distribution and the conclusions drawn from it. We present a pipeline in which the source-frame binary-black-hole population in (z,m1,m2) is represented by a normalizing flow trained directly through the hierarchical likelihood, with event posterior samples propagating measurement uncertainty and detected injections accounting for selection effects. We restrict population statements to the region supported by the injection campaign; conditioning on this region can itself induce an apparent association between mass and redshift. We therefore introduce a mutual-information diagnostic that compares the reconstruction with a redshift-independent reference under the same support restriction, testing for dependence beyond that induced by the support geometry. We validate the method on two simulated catalogues differing only in whether the characteristic primary-mass scale evolves with redshift. The reconstruction recovers the injected mass structure in both, and the benchmarks establish how the diagnostic behaves in the presence and absence of intrinsic evolution. Applied to the GWTC-5.0 catalogue, the method recovers features near 10 M⊙ and 35 M⊙, consistent with the LVK population analysis of the same catalogue, and finds no evidence for intrinsic evolution of the primary-mass spectrum with redshift. More broadly, the pipeline addresses a problem common to many observational sciences: recovering a population distribution from noisy, indirect, and selection-biased measurements of its members.
Related
- CausticFlow: An Efficient Machine Learning Framework Combining Neural Differential Equations and Normalizing Flows for Binary Microlensing Parameter Inference
- CausticFlow: An Efficient Machine Learning Framework Combining Neural Differential Equations and Normalizing Flows for Binary Microlensing Parameter Inference
- Unifying spatial correlation with hierarchical population inference to constrain the AGN channel for binary black hole mergers
- A new model for the continuum spectra of AM CVn binaries and multi-messenger inference with normalizing flows
- Physics-based phenomenological modeling of binary black hole hierarchical formation 2: Autodifferentiable functional inference of hierarchical compact-binary populations
BibTeX
@misc{iampieri2026hierarchical,
title = {{Hierarchical Population Inference with Normalizing Flows for Binary Black Holes}},
author = {Leonardo Iampieri and Simone Mastrogiovanni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11885},
eprint = {2609.11885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11885},
}
RIS
TY - UNPB
TI - Hierarchical Population Inference with Normalizing Flows for Binary Black Holes
AU - Leonardo Iampieri
AU - Simone Mastrogiovanni
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11885
UR - https://arxiv.org/abs/2609.11885
AB - Low-dimensional parametric mass models are standard in gravitational-wave population inference, but their rigidity can bias the recovered distribution and the conclusions drawn from it. We present a pipeline in which the source-frame binary-black-hole population in (z,m_1,m_2) is represented by a normalizing flow trained directly through the hierarchical likelihood, with event posterior samples propagating measurement uncertainty and detected injections accounting for selection effects. We restrict population statements to the region supported by the injection campaign; conditioning on this region can itself induce an apparent association between mass and redshift. We therefore introduce a mutual-information diagnostic that compares the reconstruction with a redshift-independent reference under the same support restriction, testing for dependence beyond that induced by the support geometry. We validate the method on two simulated catalogues differing only in whether the characteristic primary-mass scale evolves with redshift. The reconstruction recovers the injected mass structure in both, and the benchmarks establish how the diagnostic behaves in the presence and absence of intrinsic evolution. Applied to the GWTC-5.0 catalogue, the method recovers features near 10 M_⊙ and 35 M_⊙, consistent with the LVK population analysis of the same catalogue, and finds no evidence for intrinsic evolution of the primary-mass spectrum with redshift. More broadly, the pipeline addresses a problem common to many observational sciences: recovering a population distribution from noisy, indirect, and selection-biased measurements of its members.
ER -