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

TL;DR

This paper introduces Bayesian inference techniques, focusing on hierarchical models and hyper-parameters, with applications in gravitational-wave astronomy, aiming to be accessible to both novices and experts.

Contribution

It provides a comprehensive, accessible overview of Bayesian methods, including hierarchical modeling and hyper-parameters, tailored for gravitational-wave data analysis and Bayesian beginners.

Findings

Clarifies Bayesian inference fundamentals for gravitational-wave astronomy

Explains methods for model selection using Bayes factors

Details sampling techniques like MCMC and nested sampling

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