Calibrating approximate Bayesian credible intervals of gravitational-wave parameters

TL;DR

This paper introduces a calibration method for approximate Bayesian credible intervals in gravitational-wave data analysis, improving the statistical coverage of inferred parameters using neural network tools.

Contribution

The paper presents a novel calibration procedure that adjusts approximate posterior credible sets to ensure accurate coverage of the true posterior in gravitational-wave inference.

Findings

Calibration improves the statistical coverage of approximate posteriors.

Method effectively applies to high-mass binary black hole signals.

Neural networks facilitate efficient data compression and calibration.

Abstract

Approximations are commonly employed in realistic applications of scientific Bayesian inference, often due to convenience if not necessity. In the field of gravitational-wave (GW) data analysis, fast-to-evaluate but approximate waveform models of astrophysical GW signals are sometimes used in lieu of more accurate models to infer properties of a true GW signal buried within detector noise. In addition, a Fisher-information-based normal approximation to the posterior distribution can also be used to conduct inference in bulk, without the need for extensive numerical calculations such as Markov chain Monte Carlo (MCMC) simulations. Such approximations can generally lead to an inaccurate posterior distribution with poor statistical coverage of the true posterior. In this article, we present a novel calibration procedure that calibrates the credible sets for a family of approximate posterior distributions, to ensure coverage of the true posterior at a level specified by the analyst. Tools such as autoencoders and artificial neural networks are used within our calibration model to compress the data (for efficiency) and to perform tasks such as logistic regression. As a proof of principle, we demonstrate our formalism on the GW signal from a high-mass binary black hole merger, a promising source for the near-future space-based GW observatory LISA.