An introduction to Bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models

By E. Thrane, Colm Talbot. Publications Astronomical Society of Australia, 2018

413 citations recorded by the source corpus.

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 endeavour 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 generalise the formalism to discuss hyper-parameters and hierarchical models. We include extensive appendices discussing the creation of credible intervals, Gaussian noise, explicit marginalisation, posterior predictive distributions, and selection effects.

Subfields: Astronomy and Astrophysics, Atmospheric Science

View Paper: https://www.semanticscholar.org/paper/ba34e1d0b38d44da9d9af1ed3e5522ea481f1689

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Citations in the corpus

Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M ⊙ Compact Object and a Neutron Star (2024, methodology): “We employ hierarchical Bayesian inference to marginal-ize over the properties of individual events and infer the parameters of a given population model (e.g., Thrane & Talbot 2019; Mandel et al. 2019; Vitale et al. 2020).”
Constraints on the Cosmic Expansion History from GWTC–3 (2021, neutral): “Given a set of Nobs GW detections associated with the data {x} = (x1, ..., xNobs), the posterior on Φ can be expressed as (Mandel et al. 2019; Thrane & Talbot 2019; Vitale et al. 2020) p(Φ|{x}, Nobs) = p(Φ) Nobs∏ i=1 ∫ p(xi|Φ, θ)ppop(θ|Φ)dθ∫ pdet(θ,Φ)ppop(θ|Φ)dθ , (1) where p(Φ) is a prior on the…”
Bayesian inference for compact binary coalescences with bilby: validation and application to the first LIGO–Virgo gravitational-wave transient catalogue (2020, positive): “For detailed derivations of the analytically marginalized likelihood and the posterior sample reconstruction process, see Thrane & Talbot (2019).”
The Mass Distribution of Galactic Double Neutron Stars (2019, methodology): “Given a data set with N binary mass measurements, the hyperposterior distribution is given by (Thrane & Talbot 2019) ò ò p p p p L = L L L L L ( ∣{ }) ( ∣ ) ( ∣ ) ( ∣ ) ( ) ( ) ( ) p Z dm dm L m m m m d 1 d , .”
Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array (2023, methodology): “The implementation of the likelihood is described in Arzoumanian et al. (2016) and Taylor et al. 1 For an overview of the principles of Bayesian inference in gravitational-wave astronomy, see Thrane & Talbot (2019) and Taylor (2021).”