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PyCBC Inference: A Python-based parameter estimation toolkit for compact binary coalescence signals
C. M. Biwer, Collin D. Capano, Soumi De, Miriam Cabero, Duncan A. Brown, Alexander H. Nitz, V. Raymond
TL;DR
Accurately measuring compact-binary merger properties requires Bayesian inference, but binary-merger parameter spaces are high-dimensional and correlated. This paper presents PyCBC Inference, reviews its methods and module structure, and demonstrates unbiased simulated-population estimates and agreement with published first-observing-run measurements.
Problem
Accurately measuring compact-binary source properties requires Bayesian inference, while binary mergers involve high-dimensional, correlated signal parameters.
Method
PyCBC Inference is a Python-based toolkit implementing Bayesian inference modules for compact-object binary-merger parameter estimation, including likelihood evaluation and credible-interval calculations.
Results
PyCBC Inference produces unbiased parameter estimates for a simulated binary-black-hole population and posterior distributions consistent with published first-observing-run measurements.
Takeaways & Limitations
The demonstrated analyses support PyCBC Inference as a toolkit for gravitational-wave parameter-estimation studies of compact-object mergers.
Takeaways & Limitations
Percentile credible intervals impose a nonzero lower boundary, so HPD intervals may be preferable when posterior distributions are asymmetric or near a boundary.
Abstract
from arXiv · showhide
We introduce new modules in the open-source PyCBC gravitational- wave astronomy toolkit that implement Bayesian inference for compact-object binary mergers. We review the Bayesian inference methods implemented and describe the structure of the modules. We demonstrate that the PyCBC Inference modules produce unbiased estimates of the parameters of a simulated population of binary black hole mergers. We show that the posterior parameter distributions obtained used our new code agree well with the published estimates for binary black holes in the first LIGO-Virgo observing run.
1. Introduction
PyCBC Inference adds Bayesian parameter-estimation modules to the open-source PyCBC toolkit for compact-object mergers. The paper describes the methods and software, then evaluates the toolkit on simulated and observed binary black-hole events.
- Motivation: PyCBC Inference implements Bayesian inference for measuring compact-binary source parameters from gravitational-wave observations.Bayesian inference selects supported signal models and produces posterior probability densities for model parameters.
- Contribution: The paper comprehensively describes the Bayesian methods and code structure implemented in PyCBC Inference.The methods include waveform models, likelihood evaluation, sampling, independent-sample selection, and parameter estimation from posterior probabilities.
- Evaluation: The toolkit produces unbiased parameter estimates for a simulated population of binary black holes and agrees well with published first-observing-run measurements.The paper applies PyCBC Inference to simulated systems and black-hole mergers detected during the first LIGO-Virgo observing run.
2. Bayesian Inference for Binary Mergers
Bayesian inference models gravitational-wave data to estimate source parameters and compare hypotheses, while PyCBC Inference implements these calculations for detector networks. The framework addresses high-dimensional, correlated merger parameters using computationally efficient waveform models, likelihood evaluation, marginalization, and posterior summaries.
- Bayesian framework: Bayesian inference combines prior knowledge with detector data to produce posterior probabilities for gravitational-wave signal parameters.The signal hypothesis defines the source model, while the prior and likelihood encode prior parameter knowledge and the probability of the observed data given the model.
- Bayesian framework: Evidence normalizes the posterior, and the Bayes factor compares competing models by indicating which is favored and by how strongly.A Bayes factor greater than 1 favors model HA over HB.
- Binary-merger models: Binary-merger inference is difficult because the signal parameter space is large and contains degeneracies among masses, mass ratio, and spin.The chirp mass dominates at leading order, while higher-order mass-ratio effects are harder to measure and can create amplitude-dependent mass degeneracies.
- Binary-merger models: Waveform choices balance the physics being studied, computational cost, and desired model accuracy, with PyCBC Inference supporting multiple waveform families.Supported approaches include post-Newtonian, calibrated analytic, perturbative, numerical, and surrogate waveform models; full numerical simulations can be prohibitively expensive.
- Likelihood function: PyCBC Inference evaluates detector-network likelihoods under stationary, Gaussian, uncorrelated noise assumptions using frequency-domain data, waveforms, and detector noise spectra.The network data are modeled as di(t) = ni(t) + si(t), with detector-specific responses determined by antenna patterns and source location.
- Likelihood function: Analytically marginalizing over the fiducial phase reduces computational cost by a factor of 2 – 3 for suitable waveform models.This treatment assumes a uniform phase prior and is used because fiducial phase is generally a nuisance parameter.
- Posterior summaries: PyCBC Inference summarizes posterior samples with percentile credible intervals and uses Highest Posterior Density contours for two-dimensional marginal distributions.HPD intervals can be preferable for asymmetric distributions, but one-dimensional HPD credible intervals were not yet implemented for single parameters.
3. The PyCBC Inference Toolkit
PyCBC Inference integrates Bayesian sampling, waveform generation, prior evaluation, likelihood computation, and result storage into a configurable toolkit for compact-binary parameter estimation.
- Toolkit structure: PyCBC Inference provides the pycbc inference executable as the main engine for performing Bayesian inference within PyCBC.The executable initializes, executes, and saves outputs from sampler objects.
- Toolkit structure: The executable supports high-throughput and distributed execution through frameworks including HTCondor and MPI.Likelihood computation and power-spectral-density estimation can use single-threaded or parallel FFT engines.
- Toolkit structure: Configuration files specify variable parameters, priors, fixed waveform parameters, detector data, conditioning, and ensemble-MCMC settings.Command-line inputs provide the configuration and data locations, while results are stored in HDF files.
- Toolkit structure: The toolkit connects sampler, likelihood-evaluation, waveform-generation, and prior-distribution objects to sample posterior probability densities.The Sampler object obtains posterior values from LikelihoodEvaluator, which uses Generator and Distribution objects.
- Transforms and likelihood: Transform objects support sampling and waveform coordinate transformations, including efficient sampling in chirp mass and mass ratio rather than component masses.Waveform transforms also convert variables into forms accepted by waveform-model functions.
- Transforms and likelihood: LikelihoodEvaluator computes the prior-weighted likelihood, which is proportional to the posterior density when the evidence is fixed for a waveform model.This quantity can be used by sampling algorithms to calculate acceptance probabilities.
4. Validation of the Toolkit
The toolkit was validated with simulated binary-black-hole signals and astrophysical events. Its emcee pt analyses produced unbiased parameter estimates, while kombine showed greater variance and did not appear unbiased under the tested settings.
- Simulated signals: 100 simulated signals were injected into stationary Gaussian noise colored by Advanced LIGO-like power spectral densities.Signal parameters were drawn from the same prior used for GW150914, with an additional distance cut.
- Simulated signals: All parameters followed the expected 1-to-1 percentile-percentile relation in the simulated-signal validation.The kombine results had greater variance than the emcee pt results.
- Simulated signals: The aggregate KS-test p-values were 0.50 for emcee pt and 0.03 for kombine.These values quantify agreement between percentile-percentile curves and the expected relation.
- Simulated signals: PyCBC Inference produced unbiased binary-black-hole parameter estimates with emcee pt under the tested settings.Kombine did not appear unbiased for the full precessing-binary-black-hole parameter space under those settings.
- Astrophysical events: For GW150914, GW151226, and LVT151012, PyCBC Inference reported medians and 90% credible intervals for the inferred parameters.The analyses used Advanced LIGO data and the IMRPhenomPv2 waveform model.
- Astrophysical events: The event posteriors showed GW150914 with the highest component masses, GW151226 with the highest spins, and differing support for equal versus asymmetric mass ratios.Inclination and luminosity distance were generally weakly constrained, with support for face-on and face-off systems.
5. Conclusions
PyCBC Inference provides a simplified Python toolkit for compact-object binary parameter estimation, with analyses consistent with previously published event values. The paper also identifies calibration marginalization and other computational and methodological extensions as future developments.
- PyCBC Inference is a Python-based toolkit with a simplified interface for compact-object binary merger parameter estimation.
- The GW150914, GW151226, and LVT151012 analyses produced results consistent with previously published values.
- The analyses do not marginalize over calibration uncertainty in the measured strain, unlike prior work cited by the authors.
- The reported event parameters include component masses, mass ratios, effective spins, individual spins, and luminosity distances with median and 90% credible intervals.
- Future developments include calibration-error marginalization, model-selection algorithms, HPD credible intervals, and faster likelihood computation.