Comparing compact binary parameter distributions I: Methods
  Being able to measure each merger's sky location, distance, component masses,
and conceivably spins, ground-based gravitational-wave detectors will provide a
extensive and detailed sample of coalescing compact binaries (CCBs) in the
local and, with third-generation detectors, distant universe. These
measurements will distinguish between competing progenitor formation models. 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 multi-observable distributions can be fully
exploited only with very precisely calibrated detectors, search pipelines,
parameter estimation, and Bayesian model inference.
