Population-level correlations in Bayesian statistics: an illustrative model for gravitational-wave astronomy

Correlations are the new populations. After GW population analyses have (kind of) nailed down the marginal distributions of masses, spins, and redshift, the focus is now shifting to correlations between two or more parameters. Here, we take a step back and use a simple toy model to understand how correlations (or fake evidence for correlations) can emerge in hierarchical Bayesian statistics when…