Model exploration in gravitational-wave astronomy with the maximum population likelihood

Abstract

Hierarchical Bayesian inference is an essential tool for studying the population properties of compact binaries with gravitational waves. The basic premise is to infer the unknown prior distribution of binary black hole and/or neutron star parameters such component masses, spin vectors, and redshift. These distributions shed light on the fate of massive stars, how and where binaries are assembled, and the evolution of the Universe over cosmic time. Hierarchical analyses model the binary black hole population using a prior distribution conditioned on hyper-parameters, which are inferred from the data. However, a misspecified model can lead to faulty astrophysical inferences. In this paper we answer the question: given some data, which prior distribution--from the set of all possible prior distributions--produces the largest possible population likelihood? This distribution (which is not a true prior) is $\pistroke$ (pronounced "pi stroke"), and the associated \textit{maximum population likelihood} is $\Lstroke$ (pronounced "L stroke"). The structure of $\pistroke$ is a linear superposition of delta functions, a result which follows from Carath{é}odory's theorem. We show how $\pistroke$ and $\Lstroke$ can be used for model exploration/criticism. We apply this $\Lstroke$ formalism to study the population of binary black hole mergers observed in LIGO--Virgo--KAGRA's third Gravitational-Wave Transient Catalog. Based on our results, we discuss possible improvements for gravitational-wave population models.

20 pages, 9 figures

References in corpus (14)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• An improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors
• Multipolar Effective-One-Body Waveforms for Precessing Binary Black Holes: Construction and Validation
• Distinguishing Spin-Aligned and Isotropic Black Hole Populations With Gravitational Waves
• A Highly Spinning and Aligned Binary Black Hole Merger in the Advanced LIGO First Observing Run
• General maximum likelihood empirical Bayes estimation of normal means
• Cover Your Basis: Comprehensive Data-Driven Characterization of the Binary Black Hole Population
• The curious case of GW200129: interplay between spin-precession inference and data-quality issues
• The binary black hole spin distribution likely broadens with redshift
• No evidence that the majority of black holes in binaries have zero spin
• The population properties of spinning black holes using Gravitational-wave Transient Catalog 3
• Do unequal-mass binary black hole systems have larger ${\chi }_{\text{eff}}$? Probing correlations with copulas in gravitational-wave astronomy
• Limits on hierarchical black hole mergers from the most negative ${\chi }_{\mathrm{eff}}$ systems
• When models fail: an introduction to posterior predictive checks and model misspecification in gravitational-wave astronomy

Cited by in corpus (16)

• A Parameter-Free Tour of the Binary Black Hole Population
• Non-parametric inference of the population of compact binaries from gravitational wave observations using binned Gaussian processes
• Evidence for a correlation between binary black hole mass ratio and black-hole spins
• PixelPop: High Resolution Nonparameteric Inference of Gravitational-Wave Populations in Multiple Dimensions
• Fortifying gravitational-wave tests of general relativity against astrophysical assumptions
• Nonparametric analysis of correlations in the binary black hole population with LIGO-Virgo-KAGRA data
• Analysis of GWTC-3 with fully precessing numerical relativity surrogate models
• Evidence of the pair instability gap from black hole masses
• One to many: comparing single gravitational-wave events to astrophysical populations
• Do both black holes spin in merging binaries? Evidence from GWTC-4 and astrophysical implications
• Seeking Spinning Subpopulations of Black Hole Binaries via Iterative Density Estimation
• Where did Heavy Binaries Go? Gravitational-wave Populations Using Delaunay Triangulation with Optimized Complexity
• The NANOGrav 15 yr data set: Posterior predictive checks for gravitational-wave detection with pulsar timing arrays
• Are all models wrong? Falsifying binary formation models in gravitational-wave astronomy
• Probing Spin-Orbit Resonances with the Binary Black Hole Population
• Probing the peak of star formation with the stochastic background of binary black hole mergers