  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.
