Gravitational-wave astronomy with an uncertain noise power spectral density

In order to extract information about the properties of compact binaries, we must estimate the noise power spectral density of gravitational-wave data. This must be estimated from the data. Multiple estimation methods are commonly used and each has a corresponding statistical uncertainty. In order to perform increasingly precise astrophysical inference and model selection, it will be essential to account for this uncertainty. In this work, we derive the correct likelihood for one of the most widely used estimation methods in gravitational-wave transient analysis, the median average.