  Upcoming space-based coronagraphic instruments in the next decade will
perform reflected light spectroscopy and photometry of cool, directly imaged
extrasolar giant planets. We are developing a new atmospheric retrieval
methodology to help assess the science return and inform the instrument design
for such future missions, and ultimately interpret the resulting observations.
Our retrieval technique employs a geometric albedo model coupled with both a
Markov chain Monte Carlo Ensemble Sampler (emcee) and a multimodal nested
sampling algorithm (MultiNest) to map the posterior distribution. This
combination makes the global evidence calculation more robust for any given
model, and highlights possible discrepancies in the likelihood maps. As a
proof-of-concept, our current atmospheric model contains 1 or 2 cloud layers,
methane as a major absorber, and a H$_2$-He background gas. This 6-to-9
parameter model is appropriate for Jupiter-like planets and can be easily
expanded in the future. In addition to deriving the marginal likelihood
distribution and confidence intervals for the model parameters, we perform
model selection to determine the significance of methane and cloud detection as
a function of expected signal-to-noise in the presence of spectral noise
correlations. After internal validation, the method is applied to realistic
spectra of Jupiter, Saturn, and HD 99492 c, a model observing target. We find
that the presence or absence of clouds and methane can be determined with high
confidence, while parameter uncertainties are model-dependent and correlated.
Such general methods will also be applicable to the interpretation of direct
imaging spectra of cloudy terrestrial planets.
