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 postprocessing 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.
Moore, C., Gerosa, D. (2021). Population-informed priors in gravitational-wave astronomy. PHYSICAL REVIEW D, 104(8) [10.1103/PhysRevD.104.083008].
Population-informed priors in gravitational-wave astronomy
Gerosa D.
2021
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 postprocessing 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.