THE LISA OBSERVATORY WILL ALLOW US TO STUDY THE MILLI-HERTZ BAND OF THE GRAVITATIONAL WAVE SPECTRUM WHICH IS THOUGHT TO CONTAIN MANY MILLIONS OF SOURCES. THE CHALLENGE OF EXTRACTING THOUSANDS OF INDIVIDUAL SIGNALS IN THE PRESENCE OF FLUCTUATING INSTRUMENT NOISE GLITCHES AND DATA DROP-OUTS REMAINS AN UNSOLVED PROBLEM. THE SUCCESS OF THE MISSION DEPENDS ON SOLVING THIS PROBLEM WHICH IS VERY DIFFERENT AND FAR MORE CHALLENGING THAN ANYTHING THAT HAS BEEN ENCOUNTERED WITH THE GROUND-BASED LIGO-VIRGO GRAVITATIONAL WAVE DETECTORS. WE PROPOSE TO DEVELOP A FLEXIBLE TRANS-DIMENSIONAL ANALYSIS ALGORITHM THAT DYNAMICALLY DETERMINES THE NUMBER OF RESOLVABLE SOURCES AND THEIR PHYSICAL PARAMETERS WHILE SIMULTANEOUSLY MODELING THE INSTRUMENT NOISE AND ACCOUNTING FOR GAPS IN THE DATA. WE PLAN TO BUILD ON OUR EXPERIENCE USING STOCHASTIC ANALYSIS TECHNIQUES TO EXTRACT TENS OF THOUSANDS OF GALACTIC BINARY SIGNALS AND HUNDREDS OF BINARY BLACK HOLE SIGNALS FROM SIMULATED LISA DATA SETS. WE ALSO PROPOSE TO DEVELOP TECHNIQUES FOR DETECTING AND CHARACTERIZE UN-ANTICIPATED AND UN-MODELED SOURCES OF GRAVITATIONAL WAVES. THE SIGNAL EXTRACTION WILL BE DONE IN CONCERT WITH ADVANCED NOISE MODELING TECHNIQUES TO DEVELOP A PROTOTYPE GLOBAL SOLUTION TO THE LISA SCIENCE ANALYSIS PROBLEM.