Population-informed priors in gravitational-wave astronomy

TL;DR

This paper introduces a Bayesian framework for incorporating population information into the analysis of individual gravitational-wave events, addressing biases and enabling new insights into event-population correlations.

Contribution

It presents a formalism for population-informed priors derived from hierarchical Bayesian models, correcting double counting issues and enabling analysis of event-population parameter correlations.

Findings

The correction has limited impact on current gravitational-wave catalogs.

The formalism naturally accounts for selection effects.

First analysis of event-population parameter correlations in gravitational-wave data.

Abstract

We describe a Bayesian formalism for analyzing individual gravitational-wave events in light of the rest of an observed population. This analysis reveals how the idea of a "population-informed prior" arises naturally from a suitable marginalization of an underlying hierarchical Bayesian model which consistently accounts for selection effects. Our formalism naturally leads to the presence of "leave-one-out" distributions which include subsets of events. This differs from other approximations, also known as empirical Bayes methods, which effectively double count one or more events. We design a double-reweighting post-processing strategy that uses only existing data products to reconstruct the resulting population-informed posterior distributions. Although the correction we highlight is an important conceptual point, we find it has a limited impact on the current catalog of gravitational-wave events. Our approach further allows us to study, for the first time in the gravitational-wave literature, correlations between the parameters of individual events and those of the population.