  The eccentricity of a planet's orbit and the inclination of its orbital plane
encode important information about its formation and history. However,
exoplanets detected via direct-imaging are often only observed over a very
small fraction of their period, making it challenging to perform reliable
physical inferences given wide, unconstrained posteriors. The aim of this
project is to investigate biases (deviation of the median and mode of the
posterior from the true values of orbital parameters, and the width and
coverage of their credible intervals) in the estimation of orbital parameters
of directly-imaged exoplanets, particularly their eccentricities, and to define
general guidelines to perform better estimations of uncertainty. For this, we
constructed various orbits and generated mock data for each spanning $\sim 0.5
\%$ of the orbital period. We used the Orbits For The Impatient (OFTI)
algorithm to compute orbit posteriors, and compared those to the true values of
the orbital parameters. We found that the inclination of the orbital plane is
the parameter that most affects our estimations of eccentricity, with orbits
that appear near edge-on producing eccentricity distributions skewed away from
the true values, and often bi-modal. We also identified a degeneracy between
eccentricity and inclination that makes it difficult to distinguish posteriors
of face-on, eccentric orbits and edge-on, circular orbits. For the
exoplanet-imaging community, we propose practical recommendations, guidelines
and warnings relevant to orbit-fitting.
