  The problem of efficiently computing the orbital elements of a visual binary
while still deriving confidence intervals with frequentist properties is
treated. When formulated in terms of the Thiele-Innes elements, the known
distribution of probability in Thiele-Innes space allows efficient grid-search
plus Monte-Carlo-sampling schemes to be constructed for both the
minimum-$\!\chi^{2}$ and Bayesian approaches to parameter estimation. Numerical
experiments with $10^{4}$ independent realizations of an observed orbit confirm
that the $1-$ and $2\sigma$ confidence and credibility intervals have coverage
fractions close to their frequentist values. \keywords{binaries: visual -
stars: fundamental parameters - methods:statistical}
