An introduction to Bayesian inference in gravitationalwave astronomy: Parameter estimation, model selection, and hierarchical models
Abstract
This is an introduction to Bayesian inference with a focus on hierarchical models and hyperparameters. 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 gravitationalwave 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 hyperparameters and hierarchical models. We include extensive appendices discussing the creation of credible intervals, Gaussian noise, explicit marginalisation, posterior predictive distributions, and selection effects.
 Publication:

Publications of the Astronomical Society of Australia
 Pub Date:
 March 2019
 DOI:
 10.1017/pasa.2019.2
 arXiv:
 arXiv:1809.02293
 Bibcode:
 2019PASA...36...10T
 Keywords:

 methods: statistical;
 gravitational waves;
 stars: black holes;
 stars: neutron;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 16 pages, 3 figures, v8 includes erratum