Mind the gap: addressing data gaps and assessing noise mismodeling in LISA

TL;DR

This paper develops and tests methods for analyzing gapped data from the LISA gravitational wave detector, focusing on noise modeling, parameter estimation, and the impact of data gaps on signal recovery.

Contribution

It derives a likelihood function for gapped data, introduces proxies for p-p plots, and evaluates the effects of noise mismodeling and windowing on parameter estimation accuracy.

Findings

Tapering windows reduce statistical errors caused by noise mismodeling.

Assuming independence between data segments is generally valid for parameter estimation.

Fictitious correlations can lead to inconsistent parameter recovery.

Abstract

Due to the sheer complexity of the Laser Interferometer Space Antenna (LISA) space mission, data gaps arising from instrumental irregularities and/or scheduled maintenance are unavoidable. Focusing on merger-dominated massive black hole binary signals, we test the appropriateness of the Whittle-likelihood on gapped data in a variety of cases. From first principles, we derive the likelihood valid for gapped data in both the time and frequency domains. Cheap-to-evaluate proxies to p-p plots are derived based on a Fisher-based formalism, and verified through Bayesian techniques. Our tools allow to predict the altered variance in the parameter estimates that arises from noise mismodeling, as well as the information loss represented by the broadening of the posteriors. The result of noise mismodeling with gaps is sensitive to the characteristics of the noise model, with strong low-frequency (red) noise and strong high-frequency (blue) noise giving statistically significant fluctuations in recovered parameters. We demonstrate that the introduction of a tapering window reduces statistical inconsistency errors, at the cost of less precise parameter estimates. We also show that the assumption of independence between inter-gap segments appears to be a fair approximation even if the data set is inherently coherent. However, if one instead assumes fictitious correlations in the data stream, when the data segments are actually independent, then the resultant parameter recoveries could be inconsistent with the true parameters. The theoretical and numerical practices that are presented in this work could readily be incorporated into global-fit pipelines operating on gapped data.