Density estimation with Gaussian processes for gravitational wave posteriors

V D’Emilio,V Raymond,R Green

doi:10.1093/mnras/stab2623

V D’Emilio, V Raymond + Show 1 more

Open Access

https://doi.org/10.1093/mnras/stab2623

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Abstract

ABSTRACTThe properties of black hole and neutron-star binaries are extracted from gravitational waves (GW) signals using Bayesian inference. This involves evaluating a multidimensional posterior probability function with stochastic sampling. The marginal probability distributions of the samples are sometimes interpolated with methods such as 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 (GPs) 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 resampling with Hamiltonian Monte Carlo.

Highlights

The first detection of gravitational waves (GW) in 2015 (Abbott et al 2016a) sparked a new era of Astronomy
We have presented an alternative method for density estimation of marginal probability density functions (PDFs) for GW parameters
Our method combines the desirable features of histograms to the extrapolation capabilities of kernel density estimators (KDEs), within a Bayesian framework

Summary

Introduction

The first detection of gravitational waves (GW) in 2015 (Abbott et al 2016a) sparked a new era of Astronomy. Several years on from that event the number of detected GWs keeps increasing and within this decade we expect to observe O(103) signals (Abbott et al 2020b) from compact binary coalescences (CBCs). This huge progress brings with it the challenge of efficiently analysing a large number of events. To address these computational challenges, machine-learning techniques are being increasingly investigated within the field of GW physics (Cuoco et al 2020). Other work has focused on combining detection and parameter estimation with deep neural networks (Fan et al 2019) as well as using neural networks to rapidly generate surrogate waveforms (Chua, Galley & Vallisneri 2019; Khan & Green 2020)

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Conclusion