Accounting for the Known Unknowns: A Parametric Framework to Incorporate Systematic Waveform Errors in Gravitational-Wave Parameter Estimation

TL;DR

This paper introduces a parametric Bayesian framework to incorporate systematic waveform errors into gravitational-wave parameter estimation, reducing biases and improving accuracy in the presence of model uncertainties.

Contribution

It develops a parametrization method for waveform uncertainties and demonstrates how to incorporate them as priors in Bayesian PE, addressing systematic errors in GW analysis.

Findings

Errors of 1-2% in phase can bias parameter recovery.

Accounting for waveform uncertainties reduces systematic errors.

The method is validated with simulated GW signals.

Abstract

The PE for GW merger events relies on a waveform model calibrated using numerical simulations. Within the Bayesian framework, this waveform model represents the GW signal produced during the merger and is crucial for estimating the likelihood function. However, these waveform models may possess systematic errors that can differ across the parameter space. Addressing these errors in the current data analysis pipeline is an active area of research. We introduce parametrizations for the uncertainties in the amplitude and phase of the reference waveform model. When the error budget in the amplitude and phase of the waveform model, as a function of frequency, is known, it can be used as a prior distribution in the Bayesian framework. We also show that conservative priors can be used to quantify uncertainties in waveform modeling without any knowledge of waveform uncertainty error budgets. Through zero-noise injections and PE recoveries, we demonstrate that even 1%-2% of errors in relative phase to the actual waveform model, for a GW150914-like signal and advanced LIGO detector sensitivity, can introduce biases in the recovered parameters. These biases can be corrected when we account for waveform uncertainties within the PE framework. By analyzing a series of simulated signals from mergers with precessing orbits and recovering them using a non-spinning waveform model, we demonstrate that we can reduce the ratio of systematic errors to statistical errors. This approach allows us to address scenarios where specific physical effects are missing in waveform modeling. The code that implements our parametrization for performing PE is available as a Python package "pycbc_wferrors_plugin", compatible with the PyCBC open source GW analysis library.