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The recent report of an association of the gravitational-wave (GW) binaryblack hole (BBH) merger GW190521 with a flare in the Active Galactic Nuclei(AGN) J124942.3+344929 has generated tremendous excitement. However, GW190521has one of the largest localization volumes amongst all of the GW eventsdetected so far. The 90\% localization volume likely contains $7,400$unobscured AGN brighter than $g \leq 20.5$ AB mag, and it results in a $\gtrsim70\%$ probability of chance coincidence for an AGN flare consistent with the GWevent. We present a Bayesian formalism to estimate the confidence of an AGNassociation by analyzing a population of BBH events with dedicated follow-upobservations. Depending on the fraction of BBH arising from AGNs, counterpartsearches of $\mathcal{O}(1)-\mathcal{O}(100)$ GW events are needed to establisha confident association, and more than an order of magnitude more for searcheswithout followup (i.e, using only the locations of AGNs and GW events).Follow-up campaigns of the top $\sim 5\%$ (based on volume localization andbinary mass) of BBH events with total rest frame mass $\ge 50~M_\odot$ areexpected to establish a confident association during the next LIGO/Virgo/KAGRAobserving run (O4), as long as the true value of the fraction of BBH givingrise to AGN flares is $>0.1$. Our formalism allows us to jointly infercosmological parameters from a sample of BBH events that include chancecoincidence flares. Until the confidence of AGN associations is established,the probability of chance coincidence must be taken into account to avoidbiasing astrophysical and cosmological constraints.

Do LIGO/Virgo black hole mergers produce AGN flares? The case of GW190521 and prospects for reaching a confident association