A new study addresses the challenge of data gaps in gravitational-wave detectors, particularly for future missions like LISA. These gaps affect the stationarity of noise, a fundamental assumption for the Whittle likelihood method, widely used in gravitational-wave parameter inference. The research focuses on how noise mis-modeling, due to the presence of these gaps, impacts the joint inference of signal and noise parameters, a critical issue when interruptions overlap with astrophysical signals of interest.

The researchers developed an analytical and numerical framework to assess this impact, using a Fisher-matrix formalism validated against Bayesian inference. This allowed them to obtain closed-form expressions for model uncertainties and their maximum-likelihood estimates. The study examined various gap families, from long, well-tapered interruptions to short, high-rate ones, injecting massive black-hole binary signals. They showed that, except in the case of frequent gaps, the windowed covariance is well approximated by its leading diagonal for both signal and noise parameter estimation. However, by omitting the convolution, noise parameters, particularly the optical-metrology noise dominant at high frequencies, can be displaced by over an order of magnitude in power.

At the highest glitch rates, the diagonal approximation remains accurate but loses an order of magnitude in precision. To remedy this, the study proposes an exact time-domain likelihood for the surviving samples. This function can be efficiently and accurately solved via preconditioned conjugate gradient methods. This advance is crucial for missions like LISA, where the presence of gaps is an inherent feature of the data and correct inference of noise and signal parameters is essential for the detection and characterization of astrophysical sources.