Data-driven methods to explore a large space of computationally costly compact binary progenitor models

Being able to measure each merger's sky location, distance, component masses, and conceivably spins, ground-based gravitational-wave detectors will provide an extensive and detailed sample of coalescing compact binaries in the local and, with third-generation detectors, distant universe. By applying conventional Bayesian methods to an array of competing progenitor formation models, these measurements will distinguish between competing scenarios. First, however, each progenitor formation scenario must be calculated, typically at great computational cost. In practice, a sparse sample of costly scenarios will be gradually refined, guided by observations. This iterative procedure requires physically motivated and data-driven parametrizations of the model space, to quantify the similarities between a given sparse sample of scenarios; the ability for observations to distinguish between them; and to identify plausible new scenarios meriting detailed evaluation. In this paper we develop practical tools to characterize the amount of experimentally accessible information available, to distinguish between two a priori progenitor models. Using a simple time-independent model, we demonstrate the information content scales strongly with the number of observations. The exact scaling depends on how significantly mass distributions change between similar models. We develop phenomenological diagnostics to estimate how many models can be distinguished, using first-generation and future instruments. Finally, we emphasize that multiobservable distributions can be fully exploited only with very precisely calibrated detectors, search pipelines, parameter estimation, and Bayesian model inference.