When models fail: an introduction to posterior predictive checks and model misspecification in gravitational-wave astronomy

Abstract

Bayesian inference is a powerful tool in gravitational-wave astronomy. It enables us to deduce the properties of merging compact-object binaries and to determine how these mergers are distributed as a population according to mass, spin, and redshift. As key results are increasingly derived using Bayesian inference, there is increasing scrutiny on Bayesian methods. In this review, we discuss the phenomenon of \textit{model misspecification}, in which results obtained with Bayesian inference are misleading because of deficiencies in the assumed model(s). Such deficiencies can impede our inferences of the true parameters describing physical systems. They can also reduce our ability to distinguish the "best fitting" model: it can be misleading to say that Model~A is preferred over Model~B if both models are manifestly poor descriptions of reality. Broadly speaking, there are two ways in which models fail: models that fail to adequately describe the data (either the signal or the noise) have misspecified likelihoods. Population models -- designed, for example, to describe the distribution of black hole masses -- may fail to adequately describe the true population due to a misspecified prior. We recommend tests and checks that are useful for spotting misspecified models using examples inspired by gravitational-wave astronomy. We include companion python notebooks to illustrate essential concepts.

15 figures

References in corpus (4)

• BayesWave: Bayesian Inference for Gravitational Wave Bursts and Instrument Glitches
• BayesLine: Bayesian Inference for Spectral Estimation of Gravitational Wave Detector Noise
• An Optimal Strategy for Accurate Bulge-to-disk Decomposition of Disk Galaxies
• Gravitational wave detection without boot straps: a Bayesian approach

Cited by in corpus (21)

• Deep learning and Bayesian inference of gravitational-wave populations: Hierarchical black-hole mergers
• The population properties of spinning black holes using Gravitational-wave Transient Catalog 3
• Potential Subpopulations and Assembling Tendency of the Merging Black Holes
• Evidence for a correlation between binary black hole mass ratio and black-hole spins
• Consistency of the Parkes Pulsar Timing Array Signal with a Nanohertz Gravitational-wave Background
• Model exploration in gravitational-wave astronomy with the maximum population likelihood
• Starlight-polarization-based tomography of the magnetized interstellar medium: PASIPHAE's line-of-sight inversion method
• Fortifying gravitational-wave tests of general relativity against astrophysical assumptions
• Evidence of the pair instability gap from black hole masses
• One to many: comparing single gravitational-wave events to astrophysical populations
• Constraining black-hole binary spin precession and nutation with sequential prior conditioning
• Systematic errors in searches for nanohertz gravitational waves
• Reconstructing parametric gravitational-wave population fits from non-parametric results without refitting the data
• Evidence for Three Subpopulations of Merging Binary Black Holes at Different Primary Masses
• Are all models wrong? Falsifying binary formation models in gravitational-wave astronomy
• Measurement prospects for the pair-instability mass cutoff with gravitational waves
• Significant challenges for astrophysical inference with next-generation gravitational-wave observatories
• A Gaussian process framework for testing general relativity with gravitational waves
• Revealing massive black hole astrophysics: The potential of hierarchical inference with extreme mass-ratio inspiral observations
• Which black hole formed first? Mass-ratio reversal in massive binary stars from gravitational-wave data
• Gravitational-wave astronomy requires population-informed parameter estimation