Gravitational-wave astronomy requires population-informed parameter estimation

Gravitational-wave events are interpreted in terms of Bayesian posteriors for their source properties inferred under unphysical reference priors. Though these parameter estimates are important intermediate data products for downstream analyses, we demonstrate that they are generically biased and therefore should not be used for astrophysical interpretation directly, as is common. Hierarchical parameter estimation is the solution, as joint analysis of the entire catalog of observations reduces statistical uncertainties and actually informs the correct prior, with population-informed event parameters now appropriate for astrophysical interpretation. As an example, we show how the most extreme measurements from a catalog can be derived and used to identify exceptional events from previous and ongoing observing runs, pointing out they are more informative about the population than any individual event. Using LIGOVirgo-KAGRA data, we thus demonstrate that population inference is not optional to interpret gravitational-wave observations.