A reference-frequency-independent detection statistic for eccentric binary mergers is introduced and applied to GW200105, yielding ln B ≤ 0.9 in favor of the eccentric aligned-spin model over the quasi-circular precessing model.
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An introduction to Bayesian inference in gravitational-wave astronomy: parameter estimation, model selection, and hierarchical models
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abstract
This is an introduction to Bayesian inference with a focus on hierarchical models and hyper-parameters. We write primarily for an audience of Bayesian novices, but we hope to provide useful insights for seasoned veterans as well. Examples are drawn from gravitational-wave astronomy, though we endeavor for the presentation to be understandable to a broader audience. We begin with a review of the fundamentals: likelihoods, priors, and posteriors. Next, we discuss Bayesian evidence, Bayes factors, odds ratios, and model selection. From there, we describe how posteriors are estimated using samplers such as Markov Chain Monte Carlo algorithms and nested sampling. Finally, we generalize the formalism to discuss hyper-parameters and hierarchical models. We include extensive appendices discussing the creation of credible intervals, Gaussian noise, explicit marginalization, posterior predictive distributions, and selection effects.
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representative citing papers
A hierarchical Bayesian inference framework combining free-spectrum reconstruction with population-level likelihoods distinguishes finite SMBHB populations from Gaussian primordial GWB using mock PTA data.
Joint strong-lensing and population inference on resolved gravitational-wave events finds no lensed events and tightens constraints on the black-hole merger rate peak redshift and high-redshift tail.
O4a gravitational-wave data give 95% CL upper limits f_PBH ~ 1e-2 to 1e-4 for monochromatic primordial black holes with mean masses 0.6-100 M_sun, with no evidence of a PBH merger component.
Constrained polarization model for Kerr ringdown modes enables inclination inference from two-detector data for non-precessing mergers but introduces biases when applied to precessing systems.
Single-event GW parameter estimates under reference priors are population-biased; hierarchical, population-informed re-analysis is needed and changes the identification of the most extreme black holes in the catalog.
The GW-galaxy cross-correlation method, unified with spectral sirens in a harmonic framework, can measure H0 to 1% and Omega_m to 5% precision with 2 years of data from next-generation detectors like Einstein Telescope and Cosmic Explorer.
Simulations show a 40-50 solar-mass black-hole cutoff is not guaranteed to be confidently recovered from GWTC-4-like catalogs, spurious detections are unlikely, and O4 data would reduce cutoff-mass uncertainty by at least 20 percent while yielding only a lower bound on the carbon-alpha reaction rate
A two-step Bayesian reweighting scheme using Euclid galaxy locations boosts the Bayes factor for true lensed GW pairs by a factor of about 10 while lowering it for unlensed coincidences.
Hierarchical Bayesian inference on 20 high-SNR simulated binary neutron star events shows a linear lnΛ-lnQ relation suffices and constrains dynamical Chern-Simons gravity length scale to ≤10 km.
F-statistic framework analytically maximizes over distance and polarization to enable faster Bayesian inference of compact binary coalescences with a new evidence formulation that matches full frequency-domain results at lower cost.
Bayesian inference on LVK O1-O3 events with eccentric aligned-spin waveforms yields log10 Bayes factors of 1.77-4.75 favoring eccentricity for GW200129, GW190701 and GW200208_22, and >99.5% probability that at least one of 57 events is eccentric under an astrophysically motivated rate prior.
ET-Δ outperforms ET-2L on luminosity distance and source-frame masses for BBH events because its redundancy produces higher multi-detector uptime under realistic duty-cycle modeling.
Hybrid SPA-plus-FFT frequency-domain version of SEOBNRv5THM for quasi-circular spin-aligned BNS systems matches time-domain baseline accuracy while cutting computational cost for long signals.
Introduces Fisher information velocity on a PSD Riemannian manifold to decouple energy surges from spectral warps, achieving 74% higher significance than BLRMS and expanding anomaly detection by 87% on LIGO O4a data while remaining insensitive to astrophysical signals.
Spectral-siren H0 constraints from GWTC-4.0 binary black holes remain robust when the mass spectrum is permitted to evolve with redshift at current detector sensitivity.
Waveform modeling uncertainties can distort features in the binary black hole mass distribution inferred from gravitational-wave data more than statistical uncertainties.
Spin prior choices propagate into tests of GR via the 1.5PN deviation parameter δφ̂3 in a non-trivial, event-dependent way, with stronger effects for short-inspiral events and partial degeneracy with χ_eff when the deviation is included.
Bayesian parameter estimation on simulated LISA data establishes conditions for detecting displacement memory in MBHB events and projects observation rates from population models.
GW231123 data favors an overlapping two-signal model over a single merger with Bayes factors of 100-10000, mitigating waveform-dependent discrepancies and suggesting possible gravitational lensing.
Spin sorting with the default spin model distinguishes spinning and nonspinning binary black hole populations in simulations and shows real data rule out a fully nonspinning population but allow mixed ones with up to 80% nonspinning sources.
Bilby introduces a user-friendly Python library for accurate Bayesian inference on gravitational-wave signals from compact binaries and other sources, including hierarchical population modeling.
GWTC-5.0 analysis finds evidence for structure beyond a non-skewed Gaussian bulk in χ_eff, with suggestive mass-dependent excess of positive over negative spins outside the bulk at 13:1 odds in one mass bin.
GWKokab is a new modular JAX framework that uses normalizing flow samplers for efficient inference on subpopulations of compact binary mergers.
citing papers explorer
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A universal framework to identify eccentric binary mergers: GW200105 case study
A reference-frequency-independent detection statistic for eccentric binary mergers is introduced and applied to GW200105, yielding ln B ≤ 0.9 in favor of the eccentric aligned-spin model over the quasi-circular precessing model.
-
Population statistics of nanohertz gravitational wave sources
A hierarchical Bayesian inference framework combining free-spectrum reconstruction with population-level likelihoods distinguishes finite SMBHB populations from Gaussian primordial GWB using mock PTA data.
-
Joint population and strong-lensing inference for resolved gravitational-wave events probes the black-hole merger rate beyond the peak of star formation
Joint strong-lensing and population inference on resolved gravitational-wave events finds no lensed events and tightens constraints on the black-hole merger rate peak redshift and high-redshift tail.
-
Constraints on primordial black holes from the first part of LIGO-Virgo-KAGRA fourth observing run
O4a gravitational-wave data give 95% CL upper limits f_PBH ~ 1e-2 to 1e-4 for monochromatic primordial black holes with mean masses 0.6-100 M_sun, with no evidence of a PBH merger component.
-
Polarization Analysis of Ringdown Signals
Constrained polarization model for Kerr ringdown modes enables inclination inference from two-detector data for non-precessing mergers but introduces biases when applied to precessing systems.
-
Gravitational-wave astronomy requires population-informed parameter estimation
Single-event GW parameter estimates under reference priors are population-biased; hierarchical, population-informed re-analysis is needed and changes the identification of the most extreme black holes in the catalog.
-
A unified harmonic framework for dark siren cosmology
The GW-galaxy cross-correlation method, unified with spectral sirens in a harmonic framework, can measure H0 to 1% and Omega_m to 5% precision with 2 years of data from next-generation detectors like Einstein Telescope and Cosmic Explorer.
-
Measurement prospects for the pair-instability mass cutoff with gravitational waves
Simulations show a 40-50 solar-mass black-hole cutoff is not guaranteed to be confidently recovered from GWTC-4-like catalogs, spurious detections are unlikely, and O4 data would reduce cutoff-mass uncertainty by at least 20 percent while yielding only a lower bound on the carbon-alpha reaction rate
-
Improved Identification of Strongly Lensed Gravitational Waves with Host Galaxy Locations
A two-step Bayesian reweighting scheme using Euclid galaxy locations boosts the Bayes factor for true lensed GW pairs by a factor of about 10 while lowering it for unlensed coincidences.
-
Inferring neutron-star Love-Q relations from gravitational waves in the hierarchical Bayesian framework
Hierarchical Bayesian inference on 20 high-SNR simulated binary neutron star events shows a linear lnΛ-lnQ relation suffices and constrains dynamical Chern-Simons gravity length scale to ≤10 km.
-
A Robust and Efficient F-statistic-based Framework for Consistent Bayesian Inference of Compact Binary Coalescences
F-statistic framework analytically maximizes over distance and polarization to enable faster Bayesian inference of compact binary coalescences with a new evidence formulation that matches full frequency-domain results at lower cost.
-
Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA
Bayesian inference on LVK O1-O3 events with eccentric aligned-spin waveforms yields log10 Bayes factors of 1.77-4.75 favoring eccentricity for GW200129, GW190701 and GW200208_22, and >99.5% probability that at least one of 57 events is eccentric under an astrophysically motivated rate prior.
-
Impact of the Einstein Telescope's duty cycle on the estimation of binary black holes parameters
ET-Δ outperforms ET-2L on luminosity distance and source-frame masses for BBH events because its redundancy produces higher multi-detector uptime under realistic duty-cycle modeling.
-
Speed and accuracy for long signals: Frequency-domain effective-one-body waveforms for compact binary coalescences
Hybrid SPA-plus-FFT frequency-domain version of SEOBNRv5THM for quasi-circular spin-aligned BNS systems matches time-domain baseline accuracy while cutting computational cost for long signals.
-
Fisher Information Velocity: A New Geometric Channel for Precision Glitch Identification in Gravitational-Wave Detectors
Introduces Fisher information velocity on a PSD Riemannian manifold to decouple energy surges from spectral warps, achieving 74% higher significance than BLRMS and expanding anomaly detection by 87% on LIGO O4a data while remaining insensitive to astrophysical signals.
-
Gravitational-wave constraints on $H_0$ are robust to (putative) redshift evolution in the binary black hole mass spectrum at current sensitivity
Spectral-siren H0 constraints from GWTC-4.0 binary black holes remain robust when the mass spectrum is permitted to evolve with redshift at current detector sensitivity.
-
Is the Binary Black Hole Population Inference from Gravitational-Wave Data Robust?
Waveform modeling uncertainties can distort features in the binary black hole mass distribution inferred from gravitational-wave data more than statistical uncertainties.
-
The Impact of Spin Priors on Parameterized Tests of General Relativity
Spin prior choices propagate into tests of GR via the 1.5PN deviation parameter δφ̂3 in a non-trivial, event-dependent way, with stronger effects for short-inspiral events and partial degeneracy with χ_eff when the deviation is included.
-
Detectability of Gravitational-Wave Memory with LISA: A Bayesian Approach
Bayesian parameter estimation on simulated LISA data establishes conditions for detecting displacement memory in MBHB events and projects observation rates from population models.
-
GW231123: Overlapping Gravitational Wave Signals?
GW231123 data favors an overlapping two-signal model over a single merger with Bayes factors of 100-10000, mitigating waveform-dependent discrepancies and suggesting possible gravitational lensing.
-
Disentangling spinning and nonspinning binary black hole populations with spin sorting
Spin sorting with the default spin model distinguishes spinning and nonspinning binary black hole populations in simulations and shows real data rule out a fully nonspinning population but allow mixed ones with up to 80% nonspinning sources.
-
Bilby: A user-friendly Bayesian inference library for gravitational-wave astronomy
Bilby introduces a user-friendly Python library for accurate Bayesian inference on gravitational-wave signals from compact binaries and other sources, including hierarchical population modeling.
-
Evidence for additional structure in the effective spin distribution hints at multiple formation pathways in GWTC-5.0
GWTC-5.0 analysis finds evidence for structure beyond a non-skewed Gaussian bulk in χ_eff, with suggestive mass-dependent excess of positive over negative spins outside the bulk at 13:1 odds in one mass bin.
-
An Implementation to Identify the Properties of Multiple Population of Gravitational Wave Sources
GWKokab is a new modular JAX framework that uses normalizing flow samplers for efficient inference on subpopulations of compact binary mergers.
-
The first decade of gravitational-wave measurements of black hole spins
A decade of gravitational-wave data shows most merging stellar-mass black holes have small spins, with subdominant fast-spinning, misaligned, and hierarchical-merger populations.
- Horizon absorption in eccentric precessing binary black hole inspirals and its importance for gravitational wave data analysis
- Post-Newtonian inspiral waveform model for eccentric precessing binaries with higher-order modes and matter effects