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An album with hundreds of family photos holds countless stories. If you look at each picture on its own, you might easily decide that Uncle is a real giant: that day he happened to stand a step higher than everyone else. But flip through the whole album, and it becomes clear — his height is perfectly ordinary; it's just that a step showed up in a couple of frames.

Gravitational-wave detectors work in much the same way. Each registered burst is a single "snapshot" of a distant catastrophe: the merger of two black holes or neutron stars. From the waveform, scientists reconstruct what those objects were like — their masses, spin rates, and distances. But every lone signal carries an inherent ambiguity, like a shadow on the wall. Standard methods yield an estimate that can be systematically off — as if the camera lens had a subtle tilt.

The authors of the study propose not to examine the snapshots one by one, but to stitch them into a bigger picture — a joint analysis of the entire observation catalog. This approach is called hierarchical: first, general patterns are inferred from many events, then each individual measurement is refined using those patterns. It's like first realizing that everyone in the family is of average height, and only then noticing that in that particular photo, Uncle was simply standing on a stool.

Using data from the LIGO, Virgo, and KAGRA detectors, the researchers showed that without such population analysis, interpreting gravitational-wave observations remains unreliable. A single signal is just a fragment; the whole picture emerges only when we bring the entire album together.