Inferring the properties of a population of compact binaries in presence of selection effects

TL;DR

This paper introduces hierarchical Bayesian inference methods to analyze the properties and origins of compact binary populations using gravitational wave data, accounting for selection effects.

Contribution

It provides a pedagogical overview of hierarchical Bayesian inference with detailed derivations and practical examples applicable to gravitational-wave astrophysics.

Findings

Hierarchical Bayesian inference effectively models population properties.

Selection effects significantly influence population inferences.

The methods are adaptable to various fields beyond gravitational-wave astronomy.

Abstract

Shortly after a new class of objects is discovered, the attention shifts from the properties of the individual sources to the question of their origin: do all sources come from the same underlying population, or several populations are required? What are the properties of these populations? As the detection of gravitational waves is becoming routine and the size of the event catalog increases, finer and finer details of the astrophysical distribution of compact binaries are now within our grasp. This Chapter presents a pedagogical introduction to the main statistical tool required for these analyses: hierarchical Bayesian inference in the presence of selection effects. All key equations are obtained from first principles, followed by two examples of increasing complexity. Although many remarks made in this Chapter refer to gravitational-wave astronomy, the write-up is generic enough to be useful to researchers and graduate students from other fields.