  Space-based high contrast imaging mission concepts for studying rocky
exoplanets in reflected light are currently under community study. We develop
an inverse modeling framework to estimate the science return of such missions
given different instrument design considerations. By combining an exoplanet
albedo model, an instrument noise model, and an ensemble Markov chain Monte
Carlo sampler, we explore retrievals of atmospheric and planetary properties
for Earth twins as a function of signal-to-noise ratio (SNR) and resolution
($R$). Our forward model includes Rayleigh scattering, single-layer water
clouds with patchy coverage, and pressure-dependent absorption due to water
vapor, oxygen, and ozone. We simulate data at $R = 70$ and $R = 140$ from
0.4-1.0 $\mu$m with SNR $ = 5, 10, 15, 20$ at 550 nm (i.e., for
HabEx/LUVOIR-type instruments). At these same SNR, we simulate data for WFIRST
paired with a starshade, which includes two photometric points between 0.48-0.6
$\mu$m and $R = 50$ spectroscopy from 0.6-0.97 $\mu$m. Given our noise model
for WFIRST-type detectors, we find that weak detections of water vapor, ozone,
and oxygen can be achieved with observations with at least $R = 70$ / SNR$\ =
15$, or $R = 140$ / SNR$\ = 10$ for improved detections. Meaningful constraints
are only achieved with $R = 140$ / SNR$\ = 20$ data. The WFIRST data offer
limited diagnostic information, needing at least SNR = 20 to weakly detect
gases. Most scenarios place limits on planetary radius, but cannot constrain
surface gravity and, thus, planetary mass.
