  Future space telescopes may be able to directly image $\sim$10 - 100 planets
with sizes and orbits consistent with habitable surface conditions ("exo-Earth
candidates" or EECs), but observers will face difficulty in distinguishing
these from the potentially hundreds of non-habitable "false positives" which
will also be detected. To maximize the efficiency of follow-up observations, a
prioritization scheme must be developed to determine which planets are most
likely to be EECs. In this paper, we present a Bayesian method for estimating
the likelihood that any directly imaged extrasolar planet is a true exo-Earth
candidate by interpreting the planet's apparent magnitude and separation in
light of existing exoplanet statistics. As a specific application of this
general framework, we use published estimates of the discovery yield of future
space-based direct imaging mission concepts to conduct "mock surveys" in which
we compute the likelihood that each detected planet is an EEC. We find that it
will be difficult to determine which planets are EECs with $>50\%$ confidence
using single-band photometry immediately upon their detection. The best way to
reduce this ambiguity would be to constrain the planet's orbit by revisiting
the system multiple times or through a radial velocity precursor survey.
Astrometric or radial velocity constraints on the planet's mass would offer a
lesser benefit. Finally, we show that a Bayesian approach to prioritizing
targets would improve the follow-up efficiency of a direct imaging survey
versus a blind approach using the same data. For example, the prioritized
approach could reduce the amount of integration time required for the spectral
detection (or rejection) of water absorption in most EECs by a factor of two.
