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Title:
An introduction to Bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models
Authors:
Thrane, Eric; Talbot, Colm
Affiliation:
AA(Centre for Astrophysics, School of Physics and Astronomy, Monash University, VIC 3800, Australia 0000-0002-4418-3895), AB(OzGrav: The ARC Centre of Excellence for Gravitational-Wave Discovery, Clayton, VIC 3800, Australia 0000-0003-2053-5582)
Publication:
Publications of the Astronomical Society of Australia, Volume 36, id. e010 (PASA Homepage)
Publication Date:
03/2019
Origin:
CUP
Astronomy Keywords:
methods: statistical, gravitational waves, stars: black holes, stars: neutron
Abstract Copyright:
2019: Astronomical Society of Australia
DOI:
10.1017/pasa.2019.2
Bibliographic Code:
2019PASA...36...10T

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.
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