Density estimation with Gaussian processes for gravitational-wave posteriors

TL;DR

This paper introduces a novel Gaussian Process-based method for density estimation in gravitational-wave parameter inference, offering improved accuracy, uncertainty quantification, and efficiency over traditional kernel density estimators.

Contribution

It presents a new histogram-Gaussian Process hybrid technique for better density estimation of gravitational-wave posteriors, addressing limitations of existing methods.

Findings

Enhanced interpolation of non-Gaussian correlations

Bayesian uncertainty estimation for density fits

Efficient re-sampling with Hamiltonian Monte Carlo

Abstract

The properties of black-hole and neutron-star binaries are extracted from gravitational-wave signals using Bayesian inference. This involves evaluating a multi-dimensional posterior probability function with stochastic sampling. The marginal probability density distributions from which the samples are drawn are usually interpolated with kernel density estimators. Since most post-processing analysis within the field is based on these parameter estimation products, interpolation accuracy of the marginals is essential. In this work, we propose a new method combining histograms and Gaussian Processes as an alternative technique to fit arbitrary combinations of samples from the source parameters. This method comes with several advantages such as flexible interpolation of non-Gaussian correlations, Bayesian estimate of uncertainty, and efficient re-sampling with Hamiltonian Monte Carlo.