Global analysis for the LISA gravitational wave observatory

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.