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The gravitational wave sky is starting to become very crowded, with thefourth science run (O4) at LIGO expected to detect $\mathcal{O}(100)$ compactobject coalescence signals. Data analysis issues start to arise as we lookfurther forwards, however. In particular, as the event rate increases in e.g.next generation detectors, it will become increasingly likely that signalsarrive in the detector coincidentally, eventually becoming the dominant sourceclass. It is known that current analysis pipelines will struggle to deal withthis scenario, predominantly due to the scaling of traditional methods such asMonte Carlo Markov Chains and nested sampling, where the time differencebetween analysing a single signal and multiple can be as significant as days tomonths. In this work, we argue that sequential simulation-based inferencemethods can solve this problem by breaking the scaling behaviour. Specifically,we apply an algorithm known as (truncated marginal) neural ratio estimation(TMNRE), implemented in the code peregrine and based on swyft. To demonstrateits applicability, we consider three case studies comprising two overlapping,spinning, and precessing binary black hole systems with merger times separatedby 0.05 s, 0.2 s, and 0.5 s. We show for the first time that we can recover,with full precision (as quantified by a comparison to the analysis of eachsignal independently), the posterior distributions of all 30 model parametersin a full joint analysis. Crucially, we achieve this with only $\sim 15\%$ ofthe waveform evaluations that would be needed to analyse even a single signalwith traditional methods.

What to do when things get crowded? Scalable joint analysis of overlapping gravitational wave signals