  Detecting a stochastic gravitational wave background requires that we first
understand and model any astrophysical foregrounds. In the millihertz frequency
band, the predominate foreground signal will be from unresolved white dwarf
binaries in the galaxy. We build on our previous work to show that a stochastic
gravitational wave background can be detected in the presence of both
instrument noise and a galactic confusion foreground. The key to our approach
is accurately modeling the spectra for each of the various signal components.
We simulate data for a gigameter Laser Interferometer Space Antenna (LISA)
operating in the mHz frequency band detector operating with both 6- and
4-links. We obtain posterior distribution functions for the instrument noise
parameters, the galaxy level and modulation parameters, and the stochastic
background energy density. We find that we are able to detect a scale-invariant
stochastic background with energy density as low as Omega_gw = 2e-13 for a
6-link interferometer and Omega_gw = 5e-13 for a 4-link interferometer with one
year of data.
