  The stochastic gravitational-wave background (SGWB) is expected to arise from
the superposition of many independent and unresolved gravitational-wave signals
of either cosmological or astrophysical origin. The spectral content of the
SGWB carries signatures of the physics that generated it. We present a Bayesian
framework for estimating the parameters associated with different SGWB models
using data from gravitational-wave detectors. We apply this technique to recent
results from LIGO to produce the first simultaneous 95% confidence level limits
on multiple parameters in generic power-law SGWB models and in SGWB models of
compact binary coalescences. We also estimate the sensitivity of the upcoming
second-generation detectors such as Advanced LIGO/Virgo to these models and
demonstrate how SGWB measurements can be combined and compared with
observations of individual compact binary coalescences in order to build
confidence in the origin of an observed SGWB signal. In doing so, we
demonstrate a novel means of differentiating between different sources of the
SGWB.
