  We propose a new approach to Bayesian prior probability distributions
(priors) that can improve orbital solutions for low-phase-coverage orbits,
where data cover less than approximately 40% of an orbit. In instances of low
phase coverage such as with stellar orbits in the Galactic center or with
directly-imaged exoplanets, data have low constraining power and thus priors
can bias parameter estimates and produce under-estimated confidence intervals.
Uniform priors, which are commonly assumed in orbit fitting, are notorious for
this. We propose a new observable-based prior paradigm that is based on
uniformity in observables. We compare performance of this observable-based
prior and of commonly assumed uniform priors using Galactic center and
directly-imaged exoplanet (HR 8799) data. The observable-based prior can reduce
biases in model parameters by a factor of two and helps avoid under-estimation
of confidence intervals for simulations with less than about 40% phase
coverage. Above this threshold, orbital solutions for objects with sufficient
phase coverage such as S0-2, a short-period star at the Galactic center with
full phase coverage, are consistent with previously published results. Below
this threshold, the observable-based prior limits prior influence in regions of
prior dominance and increases data influence. Using the observable-based prior,
HR 8799 orbital analyses favor lower eccentricity orbits and provide stronger
evidence that the four planets have a consistent inclination around 30 degrees
to within 1-sigma. This analysis also allows for the possibility of
coplanarity. We present metrics to quantify improvements in orbital estimates
with different priors so that observable-based prior frameworks can be tested
and implemented for other low-phase-coverage orbits.
