Unbiased likelihood-free inference of the Hubble constant from light standard sirens

TL;DR

This paper demonstrates that likelihood-free inference using neural networks can unbiasedly estimate the Hubble constant from binary neutron star merger data, effectively handling selection biases without explicit likelihood calculations.

Contribution

The authors introduce a density-estimation likelihood-free inference method with neural data compression for unbiased $H_0$ estimation from merger catalogs, bypassing traditional likelihood computations.

Findings

LFI provides unbiased $H_0$ estimates despite selection effects.

Precision of LFI matches full Bayesian hierarchical models.

Marginalizing over bias increases uncertainty by only 6%.

Abstract

Multi-messenger observations of binary neutron star mergers offer a promising path towards resolution of the Hubble constant ($H_0$) tension, provided their constraints are shown to be free from systematics such as the Malmquist bias. In the traditional Bayesian framework, accounting for selection effects in the likelihood requires calculation of the expected number (or fraction) of detections as a function of the parameters describing the population and cosmology; a potentially costly and/or inaccurate process. This calculation can, however, be bypassed completely by performing the inference in a framework in which the likelihood is never explicitly calculated, but instead fit using forward simulations of the data, which naturally include the selection. This is Likelihood-Free Inference (LFI). Here, we use density-estimation LFI, coupled to neural-network-based data compression, to infer $H_0$ from mock catalogues of binary neutron star mergers, given noisy redshift, distance and peculiar velocity estimates for each object. We demonstrate that LFI yields statistically unbiased estimates of $H_0$ in the presence of selection effects, with precision matching that of sampling the full Bayesian hierarchical model. Marginalizing over the bias increases the $H_0$ uncertainty by only $6\%$ for training sets consisting of $O(10^4)$ populations. The resulting LFI framework is applicable to population-level inference problems with selection effects across astrophysics.