Normalizing Flows for Hierarchical Bayesian Analysis: A Gravitational Wave Population Study

TL;DR

This paper introduces a normalizing flow-based method for hierarchical Bayesian analysis of gravitational wave populations, demonstrating improved flexibility and robustness over traditional models on noisy LIGO/Virgo data.

Contribution

It proposes using normalizing flows to model population distributions in hierarchical Bayesian analysis, enhancing flexibility and reducing bias in gravitational wave data analysis.

Findings

Recovered population structure consistent with previous models

Less susceptible to biases from less flexible models

Effective even with small, noisy datasets

Abstract

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.