  The Laser Interferometer Space Antenna (LISA) will explore the source-rich
milli-Hertz band of the gravitational wave spectrum. In contrast to ground
based detectors, where typical signals are short-lived and discrete, LISA
signals are typically long-lived and over-lapping, thus requiring a global data
analysis solution that is very different to the source-by-source analysis that
has been developed for ground based gravitational wave astronomy. Across the
LISA band, gravitational waves are both signals {\em and} noise. The dominant
contribution to this so-called confusion noise (better termed unresolved signal
noise) is expected to come from short period galactic white dwarf binaries, but
all sources, including massive black hole binaries and extreme mass ratio
captures will also contribute. Previous estimates for the galactic confusion
noise have assumed perfect signal subtraction. Here we provide analytic
estimates for the signal subtraction residuals and the impact they have on
parameter estimation while for the first time incorporating the effects of
noise modeling. The analytic estimates are found using a maximum likelihood
approximation to the full global Bayesian analysis. We find that while the
confusion noise is {\em lowered} in the global analysis, the waveform errors
for individual sources are {\em increased} relative to estimates for isolated
signals. We provide estimates for how parameter estimation errors are inflated
from various parts of a global analysis.
