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

The gravitational wave sky is starting to become very crowded, with the fourth science run (O4) at LIGO expected to detect $\mathcal{O}(100)$ compact object coalescence signals. Data analysis issues start to arise as we look further forwards, however. In particular, as the event rate increases in e.g. next generation detectors, it will become increasingly likely that signals arrive in the detector coincidentally, eventually becoming the dominant source class. It is known that current analysis pipelines will struggle to deal with this scenario, predominantly due to the scaling of traditional methods such as Monte Carlo Markov Chains and nested sampling, where the time difference between analysing a single signal and multiple can be as significant as days to months. In this work, we argue that sequential simulation-based inference methods 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 demonstrate its applicability, we consider three case studies comprising two overlapping, spinning, and precessing binary black hole systems with merger times separated by 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 each signal independently), the posterior distributions of all 30 model parameters in a full joint analysis. Crucially, we achieve this with only $\sim 15\%$ of the waveform evaluations that would be needed to analyse even a single signal with traditional methods.