We present a framework for the analysis of direct detection planet finding missions using space telescopes. This framework generates simulations of complete missions, with varying populations of planets, to produce ensembles of mission simulations, which are used to calculate distributions of mission science yields. We describe the components of a mission simulation, including the complete description of an arbitrary planetary system, the description of a planet finding instrument, and the modeling of a target system observation. These components are coupled with a decision modeling algorithm, which allows us to automatically generate mission timelines with simple mission rules that lead to an optimized science yield. Along with the details of our implementation of this algorithm, we discuss validation techniques and possible future refinements. We apply this analysis technique to four mission concepts whose common element is a 4m diameter telescope aperture: an internal pupil mapping coronagraph with two different inner working angles, an external occulter, and the THEIA XPC multiple distance occulter. The focus of this study is to determine the ability of each of these designs to achieve one of their most difficult mission goals - the detection and characterization of Earth-like planets in the habitable zone. We find that all four designs are capable of detecting on the order of 5 Earth-like planets within a 5 year mission, even if we assume that only 1 out of every 10 stars has such a planet. The designs do differ significantly in their ability to characterize the planets they find. Along with science yield, we also analyze fuel usage for the two occulter designs, and discuss the strengths and weaknesses of each of the mission concepts.
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