  In recent years, the field of Gravitational Wave Astronomy has flourished.
With the advent of more sophisticated ground-based detectors and space-based
observatories, it is anticipated that Gravitational Wave events will be
detected at a much higher rate in the near future. One of the future data
analysis challenges is performing robust statistical inference in the presence
of detector noise transients or non-stationarities, as well as in the presence
of stochastic Gravitational Wave signals of possible astrophysical and/or
cosmological origin. The incomplete knowledge of the total noise of the
observatory can introduce challenges in parameter estimation of detected
sources. In this work, we propose a heavy-tailed, Hyperbolic likelihood, based
on the Generalized Hyperbolic distribution. With the Hyperbolic likelihood we
obtain a robust data analysis framework against data outliers, noise
non-stationarities, and possible inaccurate modeling of the noise power
spectral density. We apply this methodology to examples drawn from
gravitational wave astronomy, and in particular to synthetic data sets from the
planned LISA mission.
