  We propose parameterizing the population distribution of the gravitational
wave population modeling framework (Hierarchical Bayesian Analysis) with a
normalizing flow. We first demonstrate the merit of this method on illustrative
experiments and then analyze four parameters of the latest LIGO/Virgo data
release: primary mass, secondary mass, redshift, and effective spin. Our
results show that despite the small and notoriously noisy dataset, the
posterior predictive distributions (assuming a prior over the parameters of the
flow) of the observed gravitational wave population recover structure that
agrees with robust previous phenomenological modeling results while being less
susceptible to biases introduced by less flexible models. Therefore, the method
forms a promising flexible, reliable replacement for population inference
distributions, even when data is highly noisy.
