Sampling the full hierarchical population posterior distribution in gravitational-wave astronomy

Abstract

We present a full sampling of the hierarchical population posterior distribution of merging black holes using current gravitational-wave data. We directly tackle the most relevant intrinsic parameter space made of the binary parameters (masses, spin magnitudes, spin directions, redshift) of all the events entering the GWTC-3 LIGO/Virgo/KAGRA catalog, as well as the hyperparameters of the underlying population of sources. This results in a parameter space of about 500 dimensions, in contrast with current investigations where the targeted dimensionality is drastically reduced by marginalizing over all single-event parameters. In particular, we have direct access to (i) population parameters, (ii) population-informed single-event parameters, and (iii) correlations between these two sets of parameters. We quantify the fractional contribution of each event to the constraints on the population hyperparameters. Our implementation relies on modern probabilistic programming languages and Hamiltonian Monte Carlo, with a continuous interpolation of single-event posterior probabilities. Sampling the full hierarchical problem is feasible, as demonstrated here, and advantageous as it removes some (but not all) of the Monte Carlo integrations that enter the likelihood together with the related variances.

9+1 pages, 4+1 figures. v2/v3: match version accepted on PRD

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• Joint estimation of the cosmological model and the mass and redshift distributions of the binary black hole population with the Einstein Telescope
• Reducing systematic uncertainties in gravitational-wave population analyses by increasing the detection threshold
• The impact of precession and higher-order multipoles for gravitational wave cosmological inference
• Pushing spectral siren cosmology into the third-generation era: a blinded mock data challenge
• Exceptionality of exceptional gravitational-wave events
• The Sequential Monte Carlo goes NUTS: Boosting Gravitational-Wave Inference
• Gravitational-wave astronomy requires population-informed parameter estimation