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The next term in the numerator is the posterior for the hyperparameters given the contextual data. The point of this exercise is to show that: (1) given well-informed priors, the Bayesian odds has a clear and reliable interpretation; (2) if the prior is misinformed (i.e. does not represent our true beliefs), this interpretation becomes unreliable. POSTSUPERSCRIPT with a minimum of 0 and a maximum of 1, i.e. a power-law distribution with the same support as the correct prior, but a different spectral index. In either case, the "Bad Girls" ultimately lose, and Oxygen at best attracts the same kind of fleeting notice generated when a drunk makes a scene in a bar. POSTSUPERSCRIPT sub-hypothesis. With current nested-sampling methods, these integrals remain challenging and robust methods to calculate them are an unsolved problem which has a number of applications beyond the current work. The hyperparameterisation step in the astrophysical odds is unique to this work. In II.1, we provide a general expression for the astrophysical odds and define the component parts

POSTSUBSCRIPT, which we refer to as the contextual data. POSTSUBSCRIPT, a Bayesian odds comparing the astrophysical/terrestrial hypotheses (Farr et al., 2015; Kapadia et al., 2019; Gaebel et al., 2019). We regard this step as an important development. We use the Bilby (Ashton et al., 2019) Bayesian inference package to generate and analyse the simulated data and the dynesty (Speagle, 2019) nested-sampling package for parameter estimation and evidence evaluation. We presuppose that the data are divided into segments, each of which may contain a single binary signal. In Sec. III, we carry out a toy model demonstration to build intuition for the odds before providing a full-scale simulation study of binary black hole signals in modelled interferometer data in Sec. In Sec. II, we introduce the formalism for calculating the astrophysical odds, quantifying the probability that a data segment contains a signal of astrophysical origin versus noise. POSTSUPERSCRIPT. In the case where no contextual data is used, the astrophysical odds, Eq. POSTSUBSCRIPT are estimated in the astrophysical odds, but differs in that the work presented herein uses contextual non-time-slid data. Then, we demonstrate calculation of the astrophysical odds, showing the behaviour as a function of the amount of contextual data

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