Improving gravitational-wave parameter estimation using Gaussian process regression

TL;DR

This paper introduces a Gaussian process regression method to incorporate model uncertainties into Bayesian gravitational-wave parameter estimation, significantly improving accuracy in measuring binary black hole properties.

Contribution

The paper presents a novel application of Gaussian process regression to marginalize over model uncertainties in gravitational-wave data analysis, enhancing parameter estimation reliability.

Findings

GPR-based marginalized likelihood improves parameter estimates.

Method remains effective with varying training set sizes and covariance functions.

Approach accounts for detector noise spectral density changes.

Abstract

Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution constructed using Gaussian process regression (GPR). As an example, we apply this technique to the measurement of chirp mass using (simulated) gravitational-wave signals from binary black holes that could be observed using advanced-era gravitational-wave detectors. Unless properly accounted for, uncertainty in the gravitational-wave templates could be the dominant source of error in studies of these systems. We explain our approach in detail and provide proofs of various features of the method, including the limiting behavior for high signal-to-noise, where systematic model uncertainties dominate over noise errors. We find that the marginalized likelihood constructed via GPR offers a significant improvement in parameter estimation over the standard, uncorrected likelihood both in our simple one-dimensional study, and theoretically in general. We also examine the dependence of the method on the size of training set used in the GPR; on the form of covariance function adopted for the GPR, and on changes to the detector noise power spectral density.