As ground-based gravitational-wave (GW) detectors improve in sensitivity, gravitational-wave background (GWB) signals will progressively become detectable. Currently, searches for the GWB model the signal as a power law; however, deviations from this model will be relevant at increased sensitivity. Therefore, to prepare for the range of potentially detectable GWB signals, we propose an interpolation model implemented through a transdimensional reversible-jump Markov chain Monte Carlo algorithm. This interpolation model foregoes a specific physics-informed model (of which there are a great many) in favor of a flexible model that can accurately recover a broad range of potential signals. In this paper, we employ this framework for an array of GWB applications. We present three dimensionless fractional GW energy density injections and recoveries as examples of the capabilities of this spline interpolation model. We further demonstrate how our model can be implemented for hierarchical GW analysis on ${\mathrm{\Omega }}_{\mathrm{GW}}$.

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• Gravitational wave sources
• Gravitational waves