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Free keywords:
General Relativity and Quantum Cosmology, gr-qc, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE, Astrophysics, Instrumentation and Methods for Astrophysics, astro-ph.IM
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.
