  Most gravitational-wave signals from binary neutron star coalescences are too
weak to be individually resolved with current detectors. We demonstrate how to
extract a population of sub-threshold binary neutron star signals using
Bayesian parameter estimation. Assuming a merger rate of one signal every two
hours, we find that this gravitational-wave background can be detected after
approximately three months of observation with Advanced LIGO and Virgo at
design sensitivity, versus several years using the standard cross-correlation
algorithm. We show that the algorithm can distinguish different neutron star
equations of state using roughly seven months of Advanced LIGO and Virgo
design-sensitivity data. This is in contrast to the standard cross-correlation
method, which cannot.
