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Bayesian inference for compact binary coalescences with BILBY: Validation and application to the first LIGO--Virgo gravitational-wave transient catalogue

I. M. Romero-Shaw, C. Talbot, S. Biscoveanu, V. D'Emilio, G. Ashton, C. P. L. Berry, S. Coughlin, S. Galaudage, C. Hoy, M. Huebner, K. S. Phukon, M. Pitkin, M. Rizzo, N. Sarin, R. Smith, S. Stevenson, A. Vajpeyi, M. Arene, K. Athar, S. Banagiri, N. Bose, M. Carney, K. Chatziioannou, J. A. Clark, M. Colleoni, R. Cotesta, B. Edelman, H. Estelles, C. Garcia-Quiros, Abhirup Ghosh, R. Green, C. -J. Haster, S. Husa, D. Keitel, A. X. Kim, F. Hernandez-Vivanco, I. Magana Hernandez, C. Karathanasis, P. D. Lasky, N. De Lillo, M. E. Lower, D. Macleod, M. Mateu-Lucena, A. Miller, M. Millhouse, S. Morisaki, S. H. Oh, S. Ossokine, E. Payne, J. Powell, G. Pratten, M. Puerrer, A. Ramos-Buades, V. Raymond, E. Thrane, J. Veitch, D. Williams, M. J. Williams, L. Xiao

arXiv:2006.00714v4astro-ph.IMgr-qc

TL;DR

Gravitational-wave inference needs efficient, reliable computational methods to extract source information. This paper validates Bilby with simulated compact-binary signals and cross-validates its GWTC-1 results against LALInference, finding statistically indistinguishable results apart from two sky-area estimates.

  • Problem

    Extracting source information from gravitational-wave signals requires efficient, reliable, and accurate computational inference.

  • Method

    The study validates Bilby on simulated compact-binary signals and cross-validates analyses of eleven GWTC-1 signals against LALInference results.

  • Results

    A maximum JS divergence of JSα = 0.0026 nat was found, with statistically indistinguishable Bilby and LALInference results except for sky areas of GW170729 and GW151226.

  • Takeaways & Limitations

    Bilby is established as a modern, versatile library primed for analysis of gravitational-wave observations.

  • Takeaways & Limitations

    Reflective boundaries are implemented but not recommended because they may break detailed balance.

Abstract

from arXiv · show

Gravitational waves provide a unique tool for observational astronomy. While the first LIGO--Virgo catalogue of gravitational-wave transients (GWTC-1) contains eleven signals from black hole and neutron star binaries, the number of observations is increasing rapidly as detector sensitivity improves. To extract information from the observed signals, it is imperative to have fast, flexible, and scalable inference techniques. In a previous paper, we introduced BILBY: a modular and user-friendly Bayesian inference library adapted to address the needs of gravitational-wave inference. In this work, we demonstrate that BILBY produces reliable results for simulated gravitational-wave signals from compact binary mergers, and verify that it accurately reproduces results reported for the eleven GWTC-1 signals. Additionally, we provide configuration and output files for all analyses to allow for easy reproduction, modification, and future use. This work establishes that BILBY is primed and ready to analyse the rapidly growing population of compact binary coalescence gravitational-wave signals.

1 INTRODUCTION

The paper motivates efficient, reliable Bayesian inference for gravitational-wave signals and presents Bilby’s validation and application to compact binary coalescences. It tests simulated signals, compares with observational results, and reanalyses the eleven GWTC-1 signals using matching data and processing techniques.

  • Introduction: Gravitational-wave observations probe fundamental physics and astrophysics, while GWTC-1 contains ten binary black hole coalescences.The catalogue was produced from observations by Advanced LIGO and Advanced Virgo.
  • Introduction: Statistical inference is required to extract source information from gravitational-wave signals and constrain binary evolution and other astrophysical properties.Rapid localization is also important because electromagnetic emission can fade rapidly.
  • Introduction: Bilby is a user-friendly, modular Bayesian inference library that infers gravitational-wave source properties and adapts to diverse inference problems.The paper describes Bilby in the context of gravitational-wave astronomy and compact binary mergers.
  • Introduction: The paper develops Bilby for accurate and efficient compact binary coalescence inference and tests its validity with simulated signals and existing observational results.These tests are presented as code-validation exercises alongside comparisons with published observations.
  • Introduction: The study automates immediate candidate analysis, validates the code, and reanalyses the eleven GWTC-1 signals with identical data and processing techniques to the public LALInference results.The stated aim is to cross-validate the resulting analyses.

2 BAYESIAN INFERENCE FOR COMPACT BINARIES

This section describes Bilby’s Bayesian framework for recovering compact-binary source-parameter posteriors from gravitational-wave data. It defines the likelihood, prior, and evidence while emphasizing flexible sampler selection and the assumptions underlying the standard likelihood.

  • Bayesian framework: Bayesian inference recovers posterior probability densities for compact-binary source parameters θ given detector data and a model hypothesis H.The source parameters include quantities such as the binary components’ masses and spins.
  • Bayesian framework: The posterior combines the likelihood L(d|θ, H), prior π(θ|H), and evidence Z(d|H), with evidence normalizing parameter estimation and supporting model selection.The prior incorporates a priori knowledge, while the likelihood describes the probability of measuring detector data under the model and source parameters.
  • Likelihood: Bilby’s standard frequency-domain likelihood assumes stationary Gaussian noise and neglects the normalization term when the noise PSD is independent of model parameters.This approximation is generally suitable unless an instrument is affected by a glitch.
  • Sampling: Unlike LALInference’s customized stochastic samplers, Bilby uses adapted external off-the-shelf samplers that users can switch with minimal disruption for cross-validation.External samplers generally require tuning or adaptation for gravitational-wave inference, including sensible settings provided by Bilby.
  • Sampling: MCMC generates posterior samples through biased random walks, whereas nested sampling produces posterior samples while estimating the evidence integral from evolving live points.Nested sampling replaces the lowest-likelihood live point with a higher-likelihood point and stops after a predefined termination condition.

3 THE Bilby PACKAGE

Bilby is a modular gravitational-wave inference package whose extensions add flexible prior handling, cosmological models, computational marginalization, and scalable deployment. Its tools support efficient, reproducible analyses as detection rates increase.

  • Package architecture: Bilby’s modular architecture separates core inference functionality from gravitational-wave-specific components and supports extensions such as bilby_pipe and parallel Bilby.The core includes likelihoods, priors, sampler interfaces, result containers, and utilities.
  • Prior handling: Constraint priors let users restrict relationships such as m1 ≥ m2, equivalently enforcing the binary mass ratio q = m2/m1 ≤ 1.Constraints are stored in PriorDict objects and require a conversion_function between sampled and constrained parameters.
  • Prior handling: Conditional priors, including mass-ratio priors conditioned on primary mass, improve efficiency when equivalent constraint priors would forbid large regions of parameter space.Bilby provides ConditionalPriorDict and conditional versions of implemented priors.
  • Cosmological priors: Bilby implements cosmologically informed distance priors because luminosity-volume and comoving source-frame priors diverge substantially beyond redshift ∼1.Users can specify priors in luminosity distance, comoving distance, or redshift using Astropy-supported cosmologies, including UniformComovingVolume and UniformSourceFrame classes.
  • Computational efficiency: Analytically marginalizing over coalescence time, orbital phase, and luminosity distance reduces CBC dimensionality, speeds computation, and improves sampler convergence.These parameters are commonly marginalized because likelihood evaluations can be costly and the coalescence-time posterior may be narrow relative to its prior.
  • Scalable deployment: bilby_pipe streamlines command-line gravitational-wave parameter estimation through configuration files, while parallel Bilby distributes dynesty sampling across CPUs with MPI.Parallel sampling reduces the likelihood-evaluation burden of drawing samples from constrained priors; wall time can also decrease through marginalization or parallelization.

4 GRAVITATIONAL-WAVE TRANSIENT CATALOGUE

This section applies Bilby to all eleven GWTC-1 compact-binary events and compares its posterior samples with LALInference results. The analyses reproduce statistically indistinguishable results overall, while configuration files and posterior samples are released for reuse.

  • 4.6 Results: Bilby posterior samples, bilby_pipe configuration files, and results files are made available online to support reproduction, modification, and future use.The section also provides configuration settings files and posterior samples for direct comparisons with LALInference.
  • 4.1–4.4: Bilby analyses use event-matched default priors, dynesty sampling, five parallel analyses per event, and evidence-weighted posterior merging.For binary black holes, the waveform is IMRPhenomPv2; GW170817 uses the tidal IMRPhenomPv2_NRTidalv2 model.
  • 4.6 Results: Bilby and LALInference posterior samples are compared after reweighting the LALInference distributions by bilby_pipe default priors, using Jensen–Shannon divergence.The JS divergence ranges from 0 nat for identical information to 1 nat, according to the supplied description.
  • 4.6 Results: Six events pass the stated naive JS-divergence criterion, while GW170729 shows the largest binary-black-hole deviations in sky-position parameters, especially right ascension.Manual inspection finds posteriors with JS divergence values up to ∼0.002 nat consistent between Bilby and LALInference.
  • 4.6 Results: Bilby and LALInference are statistically indistinguishable for all reported parameters and events except the sky areas of GW170729 and GW151226.For GW170817, the maximum JS divergence is JSq = 0.0017 nat; mass-parameter posteriors agree within expected statistical fluctuations.

5 SUMMARY

Bilby is a modern, versatile Bayesian inference library that reliably produces accurate and unbiased parameter estimates for simulated gravitational-wave signals. Its GWTC-1 validation found close agreement with published LALInference posteriors, with a maximum JS divergence of 0.0026 nat for GW170729.

  • 5 SUMMARY: Bilby reliably produces accurate and unbiased parameter-estimation results when analyzing simulated gravitational-wave signals.The passage describes Bilby as primed for gravitational-wave observations.
  • 5 SUMMARY: GWTC-1 validation compared Bilby and previously published LALInference posterior distributions using the JS divergence statistic.This comparison assessed the similarity between the posterior distributions.
  • 5 SUMMARY: 0.0026 nat was the maximum JS value, measured for GW170729.The reported value is JSα = 0.0026 nat.

APPENDIX A: ADDITIONAL Bilby VALIDATION TESTS · A1 Prior sampling

Appendix A reports additional standard benchmark tests for stochastic sampling codes, including a prior-sampling test that checks whether initial samples faithfully represent the prior function. The test also contributes to Bilby’s unit-test suite and can be performed through two sampling methods.

  • APPENDIX A: ADDITIONAL Bilby VALIDATION TESTS: Appendix A adds validation tests beyond those described in the paper’s main body.These tests are described as standard benchmarks for stochastic sampling codes.
  • A1 Prior sampling: The prior-sampling test checks whether initially drawn samples faithfully represent the prior function’s shape.This assesses the distribution of samples generated from the prior.
  • A1 Prior sampling: Prior sampling serves both as a review procedure and as part of Bilby’s unit-test suite.The passage explicitly assigns both uses to the test.
  • A1 Prior sampling: Bilby provides two methods for obtaining prior samples.The passage introduces an object-level method and a null-likelihood sampler method.
  • A1 Prior sampling: The first method calls each Prior object’s sample method to generate samples by rescaling from a unit cube.This is the direct prior-object sampling approach.
  • A1 Prior sampling: The second method runs the sampler with a null likelihood using the ZeroLikelihood object.This provides an alternative route to prior sampling through the sampler.

A2 15-dimensional Gaussian

The 15-dimensional Gaussian test broadly recovers analytically expected standard deviations and evidence, while a bimodal Gaussian remains reasonably recoverable with 1000 live points but requires combining runs to mitigate mode imbalance.

  • A2 15-dimensional Gaussian: The 15-dimensional multivariate-normal likelihood reflects the typical dimensionality of binary black hole problems and provides an analytically known posterior-recovery test.All parameter means are set to zero, with a chosen covariance matrix.
  • A2 15-dimensional Gaussian: Measured standard deviations and evidence are in broad agreement with analytical expectations.This result is reported for the unimodal 15-dimensional Gaussian test.
  • A2 15-dimensional Gaussian: With more than 1000 live points, dynesty’s one-sigma credible interval is consistent with covering the true evidence 68% of the time.The quoted evidence errors are not truly Gaussian, and high credible-interval overshoot indicates fewer outliers than expected.
  • A2 15-dimensional Gaussian: For a bimodal Gaussian with modes separated by 8 standard deviations in each dimension, 1000 live points reasonably recover the evidence.The bimodal likelihood is harder to sample correctly because of its degenerate likelihood surface.
  • A2 15-dimensional Gaussian: Individual bimodal runs may bias posterior samples toward one mode, so multiple runs should be combined.The passage reports verification that none of the modes was omitted.

A3 Fiducial event simulations · APPENDIX B: RUN SETTING DETAILS

The study analyzes fiducial binary black hole and binary neutron star signals injected into simulated LIGO Hanford–Livingston design-sensitivity Gaussian noise. It specifies waveform and prior configurations, reports network SNRs and recovered parameters, and finds that nearly all true values lie within the 90% credible intervals.

  • A3 Fiducial event simulations: Two fiducial signals are analyzed: one binary black hole merger and one binary neutron star merger with tides.Both signals are added to design-sensitivity Gaussian noise in a LIGO Hanford–Livingston detector network.
  • A3 Fiducial event simulations: The binary black hole analysis uses the IMRPhenomPv2 waveform and default 4 s prior.
  • A3 Fiducial event simulations: Table A1 reports injected true values alongside recovered medians and symmetric 90% credible intervals for each parameter.
  • APPENDIX B: RUN SETTING DETAILS: The binary neutron star analysis uses the ROQ implementation of IMRPhenomPv2_NRTidalv2 with a 128 s tidal low-spin prior.
  • APPENDIX B: RUN SETTING DETAILS: 8.8 and 27.9 are the network optimal SNRs for the binary black hole and neutron star systems, respectively.
  • A3 Fiducial event simulations: Nearly all true parameter values for both simulated systems are recovered within their 90% credible intervals.

B1 Sampler settings

BILBY uses dynesty as its default nested sampler, iteratively replacing low-likelihood live points while shrinking the sampled prior region. Its sampling transitions use an MCMC random walk with chain lengths set by an autocorrelation criterion, requiring nact = 10 for these analyses.

  • Sampler choice and nested sampling: BILBY’s default sampler is dynesty, which begins with N random live points and replaces the lowest-likelihood point with a higher-likelihood prior draw.Each iteration reduces the actively sampled prior volume to the region above the discarded point’s likelihood.
  • Sampler choice and nested sampling: After uniform sampling becomes inefficient, dynesty selects new points through a custom Markov-chain Monte Carlo random walk.The transition probability is determined by the distribution of the current live points.
  • Analysis implementation: Parameter estimation used dynesty with default settings, with Bilby version 0.6.3 for binary black holes and 1.0.0 for neutron stars.The default Advanced LIGO design power spectral density changed between these Bilby versions to reflect updated detector-sensitivity predictions.
  • Evidence accuracy: 1024 live points mark the point at which evidence-error estimates reasonably reflect the true uncertainty in the unimodal Gaussian likelihood test.Fewer live points produce systematic evidence-error underestimates.
  • Sampler choice and nested sampling: nact = 10 sets the required multiple of the chain’s autocorrelation length for the analyses reported in this paper.The MCMC walker therefore takes at least n steps to draw a replacement sample, where n is determined from the autocorrelation-length requirement.

B2 Priors

The default CBC analyses sample in chirp mass and mass ratio, using priors designed to avoid thin parameter-space regions and accommodate waveform-model limitations. They adopt source-frame distance and bounded component-spin priors, with specialized low- and high-spin settings for tidal approximants and tidal-parameter sampling for GW170817.

  • Sampling parameters: Sampling directly in M and q avoids extremely thin parameter-space regions encountered when sampling in component masses.Bilby and bilby_pipe can also sample in other parameterizations, but the default GWTC-1 analyses use M and q.
  • Mass-ratio prior: The mass-ratio prior is uniform over 0.125 ⩽q ⩽1.0, with the lower bound set by IMRPhenomPv2 ROQ limitations.
  • Distance prior: The luminosity-distance prior is uniform in the source frame, motivated by gravitational-wave amplitude scaling with chirp mass and distance.This prior represents a uniform distribution of mergers in the Universe and differs from the dL^2 prior used in LALInference.
  • Spin priors: Component-spin priors are uniform from zero to mass-dependent upper limits, including 0.8, 0.88, or 0.99 for non-tidal waveform models.For tidal approximants, available upper limits are 0.05 for low-spin and 0.89 for high-spin priors, determined by the ROQ training range.
  • Tidal parameters: For GW170817, the analysis samples dimensionless tidal parameters Λ1 and Λ2 describing the primary and secondary deformabilities.

B3 Data

The analysis downloads 16384-Hz strain data, defines event-centered segments, and uses specified detector channels, including glitch-subtracted data for GW170817. It applies LAL-style time-domain down-sampling for comparison, while noting possible small bias for the lowest-mass events near the new Nyquist frequency.

  • Data access: Data segments are retrieved with GWpy using start and end times defined relative to each event’s trigger time.The trigger times and segment durations for all GWTC-1 events are provided in Table B3.
  • Detector channels: The analysis uses DCS-CALIB_STRAIN_C02 for LIGO Hanford and Livingston, except GW170817 uses glitch-subtracted DCH-CLEAN_STRAIN_C02_T1700406_v3 data.The GW170817 channel is an explicit exception to the channel used for all other events.
  • Sampling and down-sampling: 16384-Hz strain data are downloaded, while the comparison LALInference analysis used data down-sampled to 2048 Hz and integrated to 1024 Hz.16384 Hz is the native sampling frequency of advanced LIGO and advanced Virgo in the supplied description.
  • Sampling and down-sampling: For this analysis, data are down-sampled with the LAL routine because the comparison PSDs and LALInference analysis use that method.bilby_pipe also allows no down-sampling or GWpy-based down-sampling, but the analysis adopts the LAL method for consistency.
  • Sampling limitations: Down-sampling aliases data and can bias inference by suppressing and aliasing signals near the new Nyquist frequency.The lowest-mass events GW151226, GW170608, and GW170817 have frequency content close to or above that frequency, but the expected bias is small.

APPENDIX C: PRIOR REWEIGHTING

The appendix describes reweighting LALInference posterior samples to Bilby default priors for unbiased comparison. It uses rejection sampling, accounts for differing mass-parameter priors and Jacobian weights, and corrects a Solar-mass definition difference.

  • Prior reweighting: LALInference posterior samples are reweighted from priors πLI to Bilby default priors πB before comparison.The goal is to compare posterior samples without bias from differing prior choices.
  • Prior reweighting: Because Bilby uses priors flat in M and q while LALInference uses uniform component-mass priors, the procedure applies inverse-Jacobian weights.The Jacobian is given in Eq. (21) of Veitch et al. (2015).
  • Prior reweighting: Rejection sampling implements the complete reweighting procedure while preserving sample independence.The procedure is written in terms of posterior probabilities computed with Bilby and LALInference priors.
  • Prior reweighting: The comparison also accounts for differing definitions of the Solar mass M⊙ between current Bilby and the LALInference version used for public GWTC-1 samples.This correction is applied to ensure consistency with the released GWTC-1 samples.

APPENDIX D: CDF COMPARISONS FOR GWTC-1 EVENTS

Appendix D compares cumulative distribution functions (CDFs) from Bilby and LALInference for every parameter across all GWTC-1 events. The comparisons report Jensen–Shannon (JS) divergence and uncertainty, with shaded 1-, 2-, and 3-σ confidence intervals.

  • Comparison framework: CDF comparisons between Bilby and LALInference cover all parameters and all GWTC-1 events, with legends reporting JS divergence and uncertainty.Shaded regions show the 1-, 2-, and 3-σ confidence intervals.
  • GWTC-1 event comparisons: Figure D1 compares Bilby and LALInference CDFs for GW150914 and GW151012.
  • GWTC-1 event comparisons: Figure D2 compares Bilby and LALInference CDFs for GW151226 and GW170104.
  • GWTC-1 event comparisons: Figures D3 and D4 compare Bilby and LALInference CDFs for GW170608, GW170729, GW170809, and GW170814.
  • GWTC-1 event comparisons: Figures D5 and D6 compare Bilby and LALInference CDFs for GW170817, GW170818, and GW170823.

APPENDIX E: PARAMETER DEFINITIONS

Appendix E defines the compact-binary parameters implemented in Bilby and notes limited support for eccentric-orbit parameters because available frequency-domain eccentric waveforms are incomplete.

  • Parameter definitions: Bilby supports sampling compact binaries in multiple parameterisations, with definitions given in Table E1.Unless otherwise specified, these parameters can be sampled using the standard waveform model, likelihood, and conversion functions.
  • Parameter definitions: Support is limited for eccentricity e and argument of periapsis ω because available frequency-domain eccentric waveforms contain only the inspiral section.The limitation reflects less-complete LAL-Simulation eccentric waveforms compared with quasi-circular counterparts.
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