  Directly-imaged exoplanets are unexplored laboratories for the application of
the spectral and temperature retrieval method, where the chemistry and
composition of their atmospheres are inferred from inverse modeling of the
available data. As a pilot study, we focus on the extrasolar gas giant HR 8799b
for which more than 50 data points are available. We upgrade our non-linear
optimal estimation retrieval method to include a phenomenological model of
clouds that requires the cloud optical depth and monodisperse particle size to
be specified. Previous studies have focused on forward models with assumed
values of the exoplanetary properties; there is no consensus on the best-fit
values of the radius, mass, surface gravity and effective temperature of HR
8799b. We show that cloudfree models produce reasonable fits to the data if the
atmosphere is of super-solar metallicity and non-solar elemental abundances.
Intermediately cloudy models with moderate values of the cloud optical depth
and micron-sized particles provide an equally reasonable fit to the data and
require a lower mean molecular weight. We report our best-fit values for the
radius, mass, surface gravity and effective temperature of HR 8799b. The mean
molecular weight is about 3.8, while the carbon-to-oxygen ratio is about unity
due to the prevalence of carbon monoxide. Our study emphasizes the need for
robust claims about the nature of an exoplanetary atmosphere to be based on
analyses involving both photometry and spectroscopy and inferred from beyond a
few photometric data points, such as are typically reported for hot Jupiters.
